Two lasers, one red (with wavelength 633.0 nm) and the other green (with wavelen

Question

Two lasers, one red (with wavelength 633.0 nm) and the other green (with wavelength 532.0 nm), are mounted behind a 0.150-mm slit. On the other side of the slit is a white screen. When the red laser is turned on, it creates a diffraction pattern on the screen

Part A

The distance y3,red from the center of the pattern to the location of the third diffraction minimum of the red laser is 4.05 cm. How far L is the screen from the slit?

Express this distance L in meters to three significant figures.

L= m

Part B

The red laser is turned off, and the green laser is turned on. What happens to the central maximum?

It is narrower than it was for the red laser.

Part C

With both lasers turned on, the screen shows two overlapping diffraction patterns. The central maxima of the two patterns are at the same position. What is the distance y between the third minimum in the diffraction pattern of the red laser (from Part A) and the nearest minimum in the diffraction pattern of the green laser?

Express your answer in centimeters.

y = cm

It is wider than it was for the red laser.

It is narrower than it was for the red laser.

It is the same as it was for the red laser.

Part C

With both lasers turned on, the screen shows two overlapping diffraction patterns. The central maxima of the two patterns are at the same position. What is the distance y between the third minimum in the diffraction pattern of the red laser (from Part A) and the nearest minimum in the diffraction pattern of the green laser?

Express your answer in centimeters.

y = cm

Explanation / Answer

part A:

slit width=d=0.15 mm=15*10^(-5) m

order=m=3

distance from center=y=4.05 cm=0.0405 m

then distance of screen from slit is D

as for minima of order m,

y=m*lambda*D/d

where lambda=wavelength=633 nm

0.0405=3*633*10^(-9)*D/(15*10^(-5))

==>D=3.2 m

so the screen is at a distance of 3.2 m from the slit.

part B:

witdth of central maximum is 2*lambda*D/d

with D and d being constant, as wavelength for green light is lesser,

the central maximum will be narrower.

hence second option is correct.

part C:

for red light, minima are placed at:

m=1: y=1.35 cm

m=2: y=2.7 cm

m=3: y=4.05 cm

for green light, minima are placed at:

m=1: y=1.1346 cm

m=2: y=2.27 cm

m=3: y=3.4038 cm

m=4: y=4.5383 cm

so distance between third minima in diffraction pattern of the red laser and nearest minimum in the diffraction pattern of freen laser

=4.5383-4.05 =0.4883 cm

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