Behavior of Light Consider a beam of white light striking a face of an equilater

Question

Behavior of Light

Consider a beam of white light striking a face of an equilateral prism at an incident angle of theta1 = 50degree as shown. The glass that makes up the prism has an index of refraction of n = 1.446 for red light and n=1.532 for violet light. What is the angular spread of the rainbow produced by this prism? (What is the difference between the two angles theta 4 for the two colors?) During lab this week the interference pattern of a double slit set up was investigated. The criterion for the nth bright spot as counted from either side of the central maximum is sin theta n = n lambda/d. Describe how the interference pattern would be affected in the following two scenarios: Blue laser light were used instead of orange. The entire set up were submerged underwater. Consider laser light passing through a single narrow slit. What happens to the width of the central maximum of the diffraction pattern if the slit were now half as wide? Destructive Interference for the first dark spot can be determined by the equations below. In the first equation, theta dark is the angle to the first dark fringe measured from the center of the central maximum, lambda is the wavelength of laser light, and a is the aperture width. In the second equation, lambda is the height of the first dark fringe on the screen and L is the distance from the slit to the screen. Sin {theta dark) = lambda/alpha tan(theta dark) = y/L

Explanation / Answer

1) first red light

1*sin(50 degrees) = 1.446*sin theta
theta = arcsin( sin(50 degrees)/1.446) = 32 degrees

so angle withface = 90-32 = 58 degrees

58 + 60 + x = 180

x = 120 - 58 = 62 degrees

so angle with normal = 28 degrees

1.446*sin(28) = 1*sin(theta)
theta = arcsin(1.446*sin(28))= 42.75 degrees

now violet light


1*sin(50 degrees) = 1.532*sin theta
theta = arcsin( sin(50 degrees)/1.532) = 30 degrees

angle with face = 90- 30 = 60

60 + 60 + x = 180
x = 60

so angle with normal = 30
1.532*sin(30) = 1*sin theta
theta = arcsin(1.532*sin(30))= 50 degrees

so spread = 50-42.75 = 7.25 degrees

2) a) blue light has a lower wavelength so it will compress the pattern

b) a bigger n means a small wavelelngth so it will compress the pattern

3) width = 2 lambda L/a
sohalving a will double the width

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