Question

If denotes a unit vector along an incident ray and $\hat { \boldsymbol { r } }$ the unit vector along the refracted ray in a medium of refractive index μ and a unit vector normal to boundary of medium directed towards incident medium, law of refraction is

• A. . = μ( $\hat { \boldsymbol { r } }$ .)
• B. $\hat { \boldsymbol { r } }$)
• C. × $\hat { \boldsymbol { n } }$ = μ( $\hat { \boldsymbol { r } }$ ×)
• D. μ($\hat { \boldsymbol { r } }$× $\hat { \boldsymbol { n } }$

Answer 1

Answer: (C)

× $\hat { \boldsymbol { n } }$ = μ( $\hat { \boldsymbol { r } }$ ×)

Answer 2

|× $\hat { n }$ | = 1.1sin(180⁰ − i) = sini

|$\hat { \mathbf { r } }$× $\hat { n }$ | = 1.1 sin(180 − r) = sinr

Now $\frac { | \hat { i } \times \hat { n } | } { | \hat { r } \times \hat { n } | } = \frac { \sin i } { \sin r }$ = μ

∴ × = μ( $\hat { \mathbf { r } }$ × $\hat { n }$ ), as their directions are also same.

Hence (3) is correct.