Question

A medium bounded by the planes x = 0, x = a, y = b, y = –b, z = c, and z = 0 has refractive index m (x, z) = Az³ – Bx + 2. A ray of light traveling along z-axis enters the medium at point P . When the light ray emerges out, then the optical path introduced by the medium is –

• A. $\frac { \mathrm { ac } ^ { 4 } } { 4 }$
• B. 4AC⁴
• C. $\frac { \mathrm { Ba } ^ { 2 } } { 2 }$
• D. 2Ba²

Answer 1

Answer: (A)

$\frac { \mathrm { ac } ^ { 4 } } { 4 }$

Answer 2

Optical path of dz thickness = mdz = Az³ dz

Total optical path =

= $\left[ \frac { \mathrm { Az } ^ { 4 } } { 4 } \right] _ { 0 } ^ { \mathrm { c } }$ = $\frac { \mathrm { Ac } ^ { 4 } } { 4 }$