Problem 10 A diffraction grating has 200 lines/mm. It is illuminated by two monochromatic sources with wavelengths ?1 400nm and ?2 :-525nm. i) Determine the separation of the second order maxima on a screen that is 2.5m from the diffraction grating. ii) Determine the highest order for which both maxima are present.

Answers

Answer 1

The separation of the second order maxima on the screen is 0.008 m and  highest order for which both maxima are present is probably around 10.

We can use the formula for diffraction grating:

dsinθ = mλ

where d is the spacing between the grating lines, θ is the angle of diffraction, m is the order of the maximum, and λ is the wavelength of the light.

i) For the second order maximum, m = 2, and we have:

dsinθ = 2λ

The spacing between the second order maxima on the screen is given by:

y = L*tanθ

where L is the distance between the grating and the screen. Substituting sinθ = m*λ/d, we have:

y = L*(mλ)/(dcosθ)

Substituting the values given, we get:

d = 1/200 mm = [tex]510^-^6 m[/tex]

λ1 = 400 nm = [tex]410^-^7 m[/tex]

λ2 = -525 nm = [tex]-5.25*10^-^7 m[/tex]

L = 2.5 m

m = 2

For the first wavelength, we have:

sinθ1 = mλ1/d = [tex]2410^-^7/(510^-^6)[/tex] = 0.16

For the second wavelength, we have:

sinθ2 = mλ2/d =[tex]2(-5.2510^-^7)/(510^-^6[/tex]) = -0.21

The separation between the second order maxima on the screen is given by:

y = Ltanθ = Lsinθ/cosθ = L*sin(θ1-θ2)/cos(θ1+θ2)

Substituting the values, we get:

y = 2.5*sin(0.16 - (-0.21))/cos(0.16 + (-0.21)) = 0.008 m

So the separation of the second order maxima on the screen is 0.008 m.

ii) The highest order for which both maxima are present occurs when the separation between adjacent maxima is less than the distance between the two wavelengths. In other words, we want to find the maximum value of m such that:

(m+1)λ1 - mλ2 > λ2 - λ1

Substituting the values, we get:

[tex](3410^-^7) - (2*(-5.2510^-^7)) > -52510^-^9 - 400*10^-^9[/tex]

Simplifying, we get:

[tex]10^-7 > -92510^-^9^2^.^1^5[/tex]

Since the inequality is satisfied, we can say that both maxima are present for the second order.

However, since the values of the wavelengths are relatively close, we can estimate that the highest order for which both maxima are present is probably around 10.

To know more about second order maxima refer here :

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Related Questions

The electrostatic force between two charged metal spheres is 2N. If the charge on each sphere is doubled, what is the new force between the spheres?

Question 2 options:
A. 2N
B. 4N
C. 1N
D. 8

Answers

Answer:

8 N

Explanation:

The force between two charges is given by :

[tex]F=\dfrac{kq_1q_2}{d^2}[/tex]

Where

k is electrostatic constant

d is the distance between two charges

It means,

[tex]F\propto \dfrac{1}{d^2}[/tex]

When the distance is d, the force is 2 N. If the charge on each sphere is doubled, q₁' = q₂' = 2q₁ = 2q₂. New force will becomes:

[tex]F'=\dfrac{kq_1'q_2'}{d^2}\\\\F'=\dfrac{k2q_1\times 2q_2}{d^2}\\\\F'=4\times \dfrac{kq_1q_2}{d^2}\\\\F'=4\times 2\\\\F'=8\ N[/tex]

So, the new force becomes 8N. Hence, the correct option is (d).

What is the SPEED of a train that travels 15000 meters in 1200 seconds (20 minutes)?

PLEASE SHOW WORK!!!! EASY POINTS!!!!

Answers

Answer:

27.9617 mi/h

Explanation:

Speed= distance/time

S= 15000/1200

What patterns are caused by the Earth, Sun, and Moon systems?

Answers

Earth's rotation and orbit and the Moon's orbit cause observable patterns (Day and night, seasons, phases of the Moon, tides).

The Earth, Sun, and Moon systems create several patterns, including the day and night cycle, seasons, lunar phases, tides, and solar and lunar eclipses. These patterns have been studied and understood by scientists for centuries and have played an important role in shaping our understanding of the universe and our place in it. Understanding these patterns is essential in comprehending the workings of the universe and the impact they have on our planet.

What patterns are caused by the Earth, Sun, and Moon systems?

The Earth, Sun, and Moon systems create several patterns, including:

Day and Night cycle: The rotation of the Earth on its axis causes the alternating cycle of day and night as different parts of the planet face towards or away from the Sun.

Seasons: The tilt of the Earth's axis (23.5 degrees) causes the seasons to change as different parts of the planet receive varying amounts of sunlight throughout the year.

Lunar Phases: The Moon orbits the Earth, causing it to appear to change shape in the sky as different amounts of sunlight reflect off its surface.

Tides: The gravitational pull of the Moon and the Sun on the Earth's oceans creates a regular cycle of high and low tides.

Solar and Lunar Eclipses: The alignment of the Earth, Sun, and Moon can cause a shadow to be cast on one celestial body by another, resulting in either a solar or lunar eclipse.

These patterns have been studied and understood by scientists for centuries and have played an important role in shaping our understanding of the universe and our place in it.

Therefore, The day and night cycle, seasons, lunar phases, tides, and solar and lunar eclipses are just a few of the patterns that the Earth, Sun, and Moon systems produce. Scientists have been analyzing and studying these patterns for centuries, and they have had a significant impact on how we view the cosmos and our place in it. Knowing these patterns is crucial to understanding how the cosmos functions and how they affect our world.

To learn more about the heliocentric model of the Solar System click:

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Please help (choose a b or c)
(the image is attached)

In the adjacent circuit, the voltage across the terminals of the dry cell is equal to 12 V.
The value displayed by the voltmeter is:

a- 0 V
b- 12 V
c- -12 V

The two terminals that correspond to the correct connection of a voltmeter in a circuit are:

a- A and COM
b- A and V
c- V and COM​

Answers

I GEUSS A and COM is correct answer to this question

Answer:

1. (a) =0

2.(c) = v and COM

what type of em waves is fm radio? And how it is used in wireless communication?​

Answers

Answer:

Radio waves are used for wireless transmission of sound messages, or information, for communication, as well as for maritime and aircraft navigation. The information is imposed on the electromagnetic carrier wave as amplitude modulation (AM) or as frequency modulation (FM) or in digital form (pulse modulation).

Explanation:

Two objects, A and B, are in contact with one another. Initially, the temperature of A is 50 °C and the temperature of B is 100 °C. 1. **The particles of which object (A or B) initially have a greater average kinetic energy? How do you know?​

Answers

Answer:

B

Explanation:

because kinetic energy is directly proportional to temperature so the hottor the object, the more kinetic energy.

state and explain the joules law​

Answers

Answer:

Joule’s law of heating states that when a current ‘i ' passes through a conductor of resistance ‘r’ for time ‘t’ then the heat developed in the conductor is equal to the product of the square of the current, the resistance and time.

H = i 2 rt

The reason behind the heat produced is the collision of the free electrons with the lattice ions or atoms while accelerating in presence of the external electric field.

we know that

volt= work done/ total charge or v = w/q

from this we get w= vq

we know that current i = q / t

so q = it

putting this in prev equation

we get w = vit

from ohms law v = ir

putting it in prev eq we get

w = irit = i2rt joule as work is stored as heat soH = I2RT Joules

if a current carrying conductor having resistance (r) gets heated by to passing of current (i) for time (t) and the heat thereby produced be H

joules law states that

H propotional to i^ 2 when r and t are constant

H propotional to r when I and t are constant

H propotional to t when r and I constant

Ocean waves are hitting a beach with a frequency of 0.100 Hz. Their average wavelength is 15.0 m. What is their average speed?
What is the frequency of a pendulum that is moving at 30 m/s with a wavelength of 0.32 m?

Answers

Answer:

Average speed=1.5 m/s

Frequency of pendulum=93.75Hz

Explanation:

We are given

Frequency, [tex]f=0.100Hz[/tex]

Average wavelength =[tex]\lambda=15m[/tex]

Speed of pendulum, [tex]v=30m/s[/tex]

Wavelength, [tex]\lambda'=0.32m[/tex]

We have to find the average speed and frequency of pendulum.

We know that

Speed,[tex]v=\lambda f[/tex]

Using the formula

Average speed,[tex]v=15\times 0.1=1.5m/s[/tex]

Hence, the average speed =1.5m/s

Frequency, [tex]f=\frac{v}{\lambda'}[/tex]

Using the formula

[tex]f=\frac{30}{0.32}[/tex]

[tex]f=93.75Hz[/tex]

Hence, the frequency of a pendulum=93.75Hz

3. Gather data: Use the values above to fill in the first row of the table. Then run your own experiments to fill
in the last two rows.
f
d.
d,
h.
h,
ร”
S
d
de
2.0
h;
h.
2.0
s.
2.0
S
f
2.0
15
10
30

Answers

Answer:

urjshsus uevus e survey dydvd dydvdyd d dgdv gdyr yrgdvv yth yrhvthr

Explanation:

ydgdydvd yd dv ydvr dyve dysdvdyr gdvr

what's 4 x 5
i need help with this question please

Answers

4 x 5 is equal to 20. Use a calculator it’s way faster :))

Answer:

4 × 5 = 5 + 5 + 5 + 5 = 20

Explanation:

Pick one factor and add it.

A que profundidad esta nadando una persona dentro de una alberca si la presión absoluta sobre ésta es de 156kPa?

Answers

Answer:

La persona está nadando en la alberca a una profundida de 5.575 metros.

Explanation:

La presión absoluta ([tex]P_{tot}[/tex]) experimentada por la persona es la suma de la presión atmosférica ([tex]P_{atm}[/tex]) y la presión hidrostática de la columna de agua de la alberca ([tex]P_{h}[/tex]), medidas en kilopascales. Es decir,

[tex]P_{tot} = P_{atm}+P_{h}[/tex] (1)

[tex]P_{tot} = P_{atm} + \frac{\rho\cdot g \cdot z}{1000}[/tex] (2)

Donde:

[tex]\rho[/tex] - Densidad del fluido de la alberca, medida en kilogramos por metro cúbico.

[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo al cuadrado.

[tex]z[/tex] - Profundidad de la persona en la alberca, medida en metros.

Si sabemos que [tex]P_{atm} = 101.325\,kPa[/tex], [tex]\rho = 1000\,\frac{kg}{m^{3}}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] y [tex]P_{tot} = 156\,kPa[/tex], entonces la profundidad de la persona en la alberca es:

[tex]156 = 101.325 +\frac{(1000)\cdot (9.807)\cdot z}{1000}[/tex]

[tex]54.675 = 9.807\cdot z[/tex]

[tex]z = 5.575\,m[/tex]

La persona está nadando en la alberca a una profundida de 5.575 metros.

what is equilibrium state​

Answers

Answer:

A state of rest or balance due to the equal action of opposing forces.

Answer:

a state of rest or balance due to the equal action of opposing forces. equal balance between any powers, influences,etc

Explanation:

write any four importance of pressure​

Answers

Answer:

Here is your ans

Explanation:

hope it helps you tq

Mercury has the most eccentric (least circular) orbit of all the planets in the Solar System. At aphelion it is 0.467 AU from the Sun while at perihelion it is only 0.308 AU from the Sun. What is Mercury's orbital period in Earth-days?

Answers

Answer:

Mercury's orbital period is approximately 88 days

Explanation:

Mercury's orbit parameters given in the question are;

Mercury's aphelion distance, Rₐ = 0.467 AU

Mercury's perihelion distance, [tex]R_p[/tex] = 0.308 AU

Therefore, the average distance from Mercury to the Sun, 'a', is given as follows;

[tex]a = \dfrac{R_a + R_p}{2}[/tex]

By plugging in the values of 'Rₐ' and '[tex]R_p[/tex]', we get;

[tex]a = \dfrac{R_a + R_p}{2} = \dfrac{0.467 \, AU + 0.308 \, AU}{2} = 0.3875 \, AU[/tex]

a = 0.3875 AU

According to Kepler's third law, we have;

P² = k·a³

Where;

P = The orbital period of the plane

a = The average distance from Mercury to the Sun

k = Constant

When k = 1, we have;

P² = a³

∴ P = √(a³)

From which we have;

P = √(0.3875 AU)³ ≈ 0.241216804711 years

P ≈ 0.2412168 years

1 year = 365 days

∴ 0.241216804711 years = 0.241216804711 years × 365 days/year ≈ 88.0441337 days

0.241216804711 years ≈ 88.0441337 days ≈ 88 days

Mercury's orbital period, P ≈ 88 days.

The change in frequency of a wave as its source moves in relation to an observer.
A)
Ultrasound
B)
Frequency
C)
Doppler Effect
D)
Echo

Answers

Answer: B) Frequency

Explanation:

6. Suppose the resistance of your body between your right and left hands is 500,000 N. What
would be the current flowing through your body if you touched the plus and minus terminals of
a 120 V battery? The threshold of sensation for electric current through your body is about
300 PA. Would you feel the current?


HELP PLS

Answers

Explain more please (lesson)

a ball rolled a velocity of 20m/s after 5s it comes to stop what is the acceleration of the ball​

Answers

Answer:

please find the attached pdf

Explanation:

what are the unique characteristics of romantic music which are not present in Original Pilipino Music (OPM)​

Answers

Answer:

ITU Sangat bermanfaaat

All weather stations have to make weather observations at the same time of the day.

True
False

Answers

Answer:

false

Explanation:

Answer:

True

Explanation:

The answer is true do not listen to the other person they will get you wrong just look at the votes between mine and the other person's (hint like my answer and rate 5 stars so other people know what to pick)

Motion and acceleration may only be used to refer to physical objects moving or changing speed/direction

Answers

Answer:

True

Explanation:

It is TRUE that Motion and acceleration may only be used to refer to physical objects moving or changing speed/direction.

This is because if an object is not moving or changing speed/direction to a determined point of reference, the object is considered to be at rest or motionless, thereby, with no absolute point of reference, absolute motion or acceleration cannot be distinguished.

5. A car accelerates from 0 to 72 km/hour in 8.0 seconds. What is the car's acceleration?

Answers

Answer:

2.5 m/s

Explanation:

There are calculators online that can help you easily calculate the accerlation.

1. Compare the speed that light waves travel in air to the speed that sound waves travel in the air. How many times faster do light waves travel in air in comparison to sound waves in air?
Water-1500 meters per second
steel-5000 meters per second
Air-335 meters per second

Answers

Answer:

895522 times faster.

Explanation:

From the question given above, the following data were obtained:

Speed of sound in air (v) = 335 m/s

Speed of light in air (c) = 3×10⁸ m/s

How many times faster =.?

To obtain how many times faster light travels in air than sound, do the following

c : v => 3×10⁸ : 335

c/v = 3×10⁸ / 335

c/v = 895522

Cross multiply

c = 895522 × v

From the illustrations made above, we can see that the speed of the light in air (c) is 895522 times the speed of sound in air.

Thus, light travels 895522 times faster than sound in air.

If a girl walks 6km due west changes directions and walk another 5km due north. Find her displacement in both magnitude and direction

Answers

Answer:

the girl's displacement in both magnitude and direction is 7.81 m at 50.2⁰ North west.

Explanation:

Given;

6km due west, and

5km due north

The magnitude of her displacement is calculated by forming a right angled triangle. The hypotenuse side of the triangle is the girl's displacement.

d² = 5² + 6²

d² = 25 + 36

d² = 61

d = √61

d = 7.81 m

The direction of the girl is calculated as;

[tex]tan \ \theta = \frac{6}{5} \\\\tan \ \theta = 1.2\\\\\theta = tan^{-1} (1.2)\\\\\theta = 50.2^0[/tex]

Therefore, the girl's displacement in both magnitude and direction is 7.81 m at 50.2⁰ North west.

calculate the pressure exerted on the floor when an elephant who weighs 2400N stands on one foot which has an area of 0.4m squared​

Answers

Answer:

6000pa

Explanation:

force= 2400N

area= 0.4m

pressure=?

now,

p= f/a

p= 2400/ 0.4

therefore,P=6000 pa.

the Himalayas are the highest mountain in the world (positive)​. grammar question

Answers

Answer:

positive degree:

No other peak of the Himalayas is as high as Mount everest

how you would orient the magnets and what you would do with the magnets to achieve maximum repulsion

Answers

The orientation of the magnets that gives the strongest repulsion because these poles and facing each other that is then leaves highest flux density of the poles for a force of repulsion to be very high

True or false. Your weight will change on the moon

Answers

The answer to this is true
hi! i searched online, and it says an object on the moon weighs less than it does on earth, so true.

hope this helps!:)

If a storm is 7.5 kilometers away, how much time is expected between observations of lightning and thunder?

Answers

Answer. Time taken to hear the thunder is : 7500 / 343 = 21.88 Seconds.

Answer:

≈ 22 seconds

Explanation:

7,5 km = 7500 m

Speed of light 300 000 000 m/s (for lightning)

Speed of sound 343 m/s (for thunder)

time = distance / speed

lightning time = 7500 m / 300 000 000 m/s = 0.000025 s

thunder time = 7500 m / 343 m/s ≈ 22 s

thunder time - lightning time = 22 s - 0.000025 s ≈ 22 s


Long Answer Type Questions
1 Can you differentiate between opaque, transparent and translucent objects
2 What is reflection of light?
3. What are the conditions for a shadow to be formed?
4. Prove through an experiment that light travels in straight lines.
5. What is pinhole camera? Explain its working with the help of a diagram
6. What are the main differences between a reflected image and shadows?​

Answers

(1).....opaque -object that not allow light to pass through it

we can't look through opaque objects

ex..wall

translucent... objects that all some light to pass through it

we can partially see through it

ex...coloured glass window

transparent... objects that wholly allow light to pass through it

we can clearly see through it

ex...glass of specs

(2)..the bouncing back of light from a smooth polished surface is called reflection of light

(3)/.....there must be a solid ,opaque to block light

there must be a source of light

there must be a surface to have shadow on it..

(6)...reflected images r formed by light reflection from a smooth polished surface while shadows are formed by blockage of light by an solid,opaque object...

Explanation:

we should talk here thanks

The ability of a halogen to react with a metals to form a salt is an example of a ________________ property.

Answers

The answer is a CHEMICAL property.
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