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# A parallel beam of monochromatic light is incident on a glass slab at an angle of incidence 60o. Find the ratio of width of the beam in the glass to that in the air if refractive index of glass is 3/2. - Physics

#### Question

A parallel beam of monochromatic light is incident on a glass slab at an angle of incidence 60o. Find the ratio of width of the beam in the glass to that in the air if refractive index of glass is 3/2.

#### Solution

Given: i = 60°, μg = 1.5,

Let dg = width of beam in glass slab,

da = width of beam in air

To find: Ratio of widths (d_g/d_a)

Formulae:

i. mu_g=sini/sinr

ii. d_g/d_a=cosr/cosi

Calculation: From formula (i),

sin r = sin i/μg

∴ sin r = sin60°/1.5 = 0.8660/1.5 = 0.5773

∴ r = sin-1 (0.5773) = 35°16'

From formula (ii),

d_g/d_a=cosr/cosi=(cos35^@16')/cos60^@

therefore d_g/d_a=0.8164/0.5=1.633

therefored_g/d_a=1.633:1

∴ Ratio of the widths of beam = 1.633 : 1

The ratio of widths of the beam in glass to that in air is 1.633 : 1.

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