Monochromatic green light, of wavelength 500 nm, illuminates two parallel narrow slits 7.70 mm apart. Calculate the angular deviation ( θin Fig. 35-10) of the third-order (m=3)bright fringe (a) in radians and (b) in degrees.

Short Answer

Expert verified

a. The angular separation in radian is 0.214rad.

b. The angular separation in degrees is 12.28°.

Step by step solution

01

Write the given data from the question

The wavelength, λ=550nm.

The order of the bright fringe, m=3.

The distance between the slits, d=7.7μm.

02

Determine the formulas to calculate the angular separation in the degrees and radian

Young's double-slit experiment. When monochromatic light passing through two narrow slits illuminates a distant screen, a characteristic pattern of bright and dark stripes is observed. This interference pattern is caused by the superposition of overlapping light waves originating from the two slits.

The condition for the maxima in Young’s experiment is given as follows.

dsinθ=mλ …… (1)

Here, d is the distance between the slits, λ is the wavelength, m is the order and θis the angular separation.

The expression to calculate the angular separation in degrees is given as follows.

θdeg=180π×θ …… (2)

03

Calculate the angular separation in radian:

a.

For the small angle, sinθθ.

Calculate the angular separation.

Substitute 7.7μm for d, 3 for m, 550 nm for λ, and θfor sinθinto equation (1).

7.7×10-6×θ=3×550×10-9

θ=3×550×10-97.7×10-6=1650×10-37.7=0.214rad

Hence, the angular separation in radian is 0.214rad.

04

Calculate the angular separation in degrees

Calculate the angular separation.

Substitute 0.214radfor θinto equation (2).

θdeg=180π×0.214=38.52π=12.28°

Hence,the angular separation in degrees is 12.28°.

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Most popular questions from this chapter

In Fig. 35-48, an airtight chamber of length d=5.0cm is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of wavelength l λ=500nm is used. Evacuating the air from the chamber causes a shift of 60 bright fringes. From these data and to six significant figures, find the index of refraction of air at atmospheric pressure.

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