Please answer all the questions thoroughly and explain how you answered the ques

Question

Please answer all the questions thoroughly and explain how you answered the question. Answer all the questions.

7. (A) Show the spacing of two consecutive dark fringes.

(B) In Young's double-split experiment, suppose that a coherent light of wavelength 633 nm. is used, the split spacing is 0.05 mm., and the screen is 2 m. from the slits. Find the distance along the screen between the second bright fringe and the fifth dark fringe.

8. A diffraction grating disperses white light so that the red wavelength (650 nm.) appears in the second-order pattern (bright fringes) at theta=20 degrees.

(A) Find the so-called grating constant, i.e., the number of slits in cm.

(B) Determine whether or not the visible light of the third-order pattern appears at theta = 20 degrees.

Explanation / Answer

7)

path difference for constructive interfrence,

d*sin(theta) = m*lamda (m = 0,1,2,3,4,.....)

here, theta is small.

so, sin(theta) = tan(theta) = y/R

here, R ---> distance from sltd to screen.

let y1 is the distance of first bright fringe from center and

y2 is the distance of second bright fringe from center and

d*y1/R = 1*lamda

y1 = lamda*R/d

y2 = 2*lamda*R/d

A) fringe width, beta = y2-y1 = lamda*R/d

B) for second bright fringe y2 = 2*lamda*R/d
   = 2*633*10^-9*2/0.05*10^-3
   = 5.064 cm
for fifth dark fringe, y = 5*lamda*R/d

= 5*633*10^-9*2/0.05*10^-3

= 15.192 cm

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