Red light of wavelength 630 nm passes through two slits and then onto a screen t

Question

Red light of wavelength 630 nm passes through two slits and then onto a screen that is 1.3 m from the slits. The center of the 3rd order bright band on the screen is separated from the central maximum by 0.90 cm.

a) Determine the frequency of the light.

b) Determine the slit separation.

c) Determine the angle of the 3 rd order bright band.

d) Suppose the entire set-up is submerged in water. For each of the following quantities, determine if they remain the same or if they change. If they change, determine what the under-water value is for:

—Wavelength of light

—Frequency of light

—Slit separation

—Distance from central maximum to 3rd order bright band

—Angle of the 3rd-order bright band

Explanation / Answer

A)

f=c/?

f=(3x10^8)/(630x10^-9) = 4.76x10^14 Hz

B)

d=k?/sin?

k=3

?=arctan(0.90x10^-2/1.3)=0.3967 degree

then

d=3*630x10^-9/sin(0.3967)

d= 2.73x10^-4 m = 0.273 mm

C)

d=k?/sin?

?=arcsin(k?/d)

k=3

d=0.273 mm

then

?=arcsin(3*630x10^-9/0.273x10^-3)

?=0.3967 degree

D)

Index of refraction of water n = 1.33

—Wavelength of light: decreases

new wavelength = 630/1.33 = 474 nm

—Frequency of light: same

—Slit separation: same

—Distance from central maximum to 3rd order bright band:

y = (3*474*10^-9*1.3)/( 2.73x10^-4) = 6.77 x 10^-3 m

—Angle of the 3rd-order bright band:

?=arcsin(3*474x10^-9/0.273x10^-3) = 0.2984

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