Aspecial system is set up in a lab that lets its user select any wavelength between 400nm and 700 nm with constant intensity. this light is directed at a thin glass film (n =1.53) with a thickness of 350 nm and that is surrounded by air. as one scans through these possible wavelengths, which wavelength of light reflected from the glass film will appear to be the brightest, if any?

a) 428 nm

b) 535 nm

c) 657 nm

d) 700 nm

e) since the intensity of the light is constant,
all wavelengths of light reflected from the glass will appear to be the same.

Explanation:

The case relates to interference in thin films , in which we study interference of light waves reflected by upper and lower surface of a medium or glass.

For constructive interference , the condition is

2μt = ( 2n+1)λ/2

μ is refractive index of glass , t is thickness , λ is wavelength of light.

putting the given values

2 x 1.53 x 350 x 10⁻⁹ = ( 2n+1) λ/2

λ = 2142nm /  ( 2n+1)

For n = 2

λ = 428 nm

This wave length will have constructive interference making this light brightest of all .

For n = 1

λ = 714  nm

So second largest  brightness will belong to 700 nm wavelength.

the answer is b ) square root of 5

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s