Question

#2

a. Consider a Michelson interferometer with one fixed arm and one moveable arm, both of length 5 m. If 300 nm laser light is shown through the device, what percentage change in the length of the movable arm will shift the detector from constructive to destructive interference?

b. A telescope is looking at a 2 star system. If the stars are 1.5 x 10^13 m apart and 9 x 10^16 m away, how big does the telescope opening have to be to resolve the two stars?

c. If red light (lambda = 800 nm) and violet light (lambda = 400 nm) are alternately shown through a slit with width 1 mm, find the distance between the first minima for these different lights on a screen 5 m away.

Answer 1

a) For constructive interference to occur, both the arms will have to be at the same length(or a difference equal to the wavelength).

So, constructive interference can occur when L' = L = 5 m

Destructive interference occurs when the difference in length is an odd multiple of

Here, wavelength = 300 nm

So, the first destructive interference occurs at

L' = L -

So, change in length of the movable arm = 300*10^-9/2 = 150*10^-9

Percentage change = 100*(150*10^-9)/5 = 3*10^-6 %

b) The stars are 1.5*10¹³ m apart.

They are at a distance of 9*10¹⁶ m

Using angle = arc/radius, the angular separation between the stars is

The angle in arc second is given by

the diameter of the telescope in centimeters is then given by

c) For a single slit diffraction, the first minima occurs when

Where a is the slit width.

For small angle,

Using angle = arc/radius,

where s is the distance to the screen.

Here, a = 1 mm = 0.001 m

s = 5 m

So,

For red light,

For violet light,

So, separation between minima = 4-2 = 2mm