Question

Glass has refractive index μ with respect to air and the critical angle for a ray of light going from glass to air is θ. If a ray of light is incident from air on the glass with angle of incidence θ corresponding angle of refraction is ______.

Options

• sin^-1(μ)

• `sin^-1 (1/mu^2)`

• `sin^-1 (1/sqrtmu)`

• `sin^-1 (1/mu)`

Answer 1

Glass has refractive index μ with respect to air and the critical angle for a ray of light going from glass to air is θ. If a ray of light is incident from air on the glass with angle of incidence θ corresponding angle of refraction is `underline(sin^-1 (1/mu^2))`.

Explanation:

Rofractive index of glass with respect to air=µ Critical angle = θ

`therefore mu = 1/(sin theta)`    ...(i)

When a ray of light incident from air on the glass with angle of incidence θ. If r be the angle of refraction, then by Snell's law,

`mu = (sin theta)/(sin "r")`

`=> sin "r" = (sin theta)/mu = (1//mu)/mu`   ....[from Eq. (i)]

`=> sin "r" = 1/mu^2`

r = `sin^-1 (1/mu^2)`