Question

A mixture of light wave having wavelength 560nm and 400nm

Answer 1

Let nth minima of 400 nm wave coincides with mth minima of 560 nm wave.

Then,

(2n-1)(400/2) - (2m-1)(560/2)

2n-1 /2m-1  = 7/5 =14/10 ....

2n-1= 7

n= 4

2m-1=5

m=3

That is, 4th minima of 400 nm wave coincides with 3rd minima of 560 nm wave.

Location of this minima is-

y1 =[ (2×4-1).(1000).(400×10-6 ) ] / 2×0.1           (given,d=0.1 )

= 14 mm

Next 11th minima of 400 nm wave will coincides with 8th minima of 560 nm wave.

Location of this second minima is-

y2 = [(2×11-1).(1000).(400×10-6 )] /2×0.1

= 42 mm

So, the distance  between two sucessive regions of complete darkness is -

y2 - y1 = 42-14 = 20 mm

 

Answer 2

Light of wavelength 500nm in air ,enters a glass plate of refractive index 1.5 .

Find:-(i)speed

(ii)frequency and 

(iii)wavelength of light in glass

Assume that the frequency of light remains the same in both media.