Question

The critical angle for light going from medium 'x' to medium 'y' is 'θ'. The speed of light in medium 'x' is 'v_x'. The speed of light in medium 'y' is ______.

Options

• `"v"_x/(tan theta)`

• v_x sin θ

• v_x tan θ

• `"v"_x/(sin theta)`

Answer 1

The critical angle for light going from medium 'x' to medium 'y' is 'θ'. The speed of light in medium 'x' is 'v_x'. The speed of light in medium 'y' is `underline("v"_x/(sin theta))`.

Explanation:

The critical angle is that angle on incidence in the denser medium for which the angle of refraction in rarer medium is 90°, i.e.

`(sin theta)/(sin 90^circ) = mu_"y"/mu_x`

`=> sin theta = mu_"y"/mu_x`    ...(i)

where, µ = refractive index of medium.

Also, µ = `"speed of light in vacuum"/"speed of light in medium" = "c"/"v"`     ...(ii)

From Eqs. (i) and (ii), we get

sin θ = `"c"/"v"_"y" xx "v"_x/"c" = "v"_x/"v"_"y"`

`=> "v"_"y" = "v"_"x"/sin theta`

Thus, the speed of light In medium y is `"v"_"x"/sin theta`.