A glass slab of thickness 10( 3 + 1) cm and refractive index 3 is completely immersed in a transparent liquid of refractive index 2 . A light ray traveling through the liquid strikes the slab at an angle of incidence of 60^ . The lateral shift of the emergent ray when it enters back into the liquid is _____ cm .

Step-by-step solution

Applying Snell's law at the liquid-glass boundary: _l i = _g r 2 60^ = 3 r 2 ( 3 2 ) = 3 r r = 1 2 r = 45^ The lateral shift d is given by: d = t (i - r) r Substituting the values: d = 10( 3 + 1) (60^ - 45^ ) 45^ d = 10( 3 + 1) 15^ 1/ 2 = 10 2 ( 3 + 1) 15^ Using the trigonometric value 15^ = 3 - 1 2 2 : d = 10 2 ( 3 + 1) ( 3 - 1 2 2 ) d = 5 ( 3 + 1)( 3 - 1) = 5(3 - 1) = 10 cm . Answer: 10