Two rays travelling parallel to the principal axis strike a thick large plano-convex lens having a refracive index of `1.60`.If the spherical face has a radius of curvature of magnitude `20.0`cm and th two rays are `h_(1)=0.500cm`and `h_(2)=12.0cm` from the principal axis ,find the difference in the positions where they cross the principal axis .Assume that the ray incident at height `h_(2)`is incident at the periphery.

Answer

`21.3cm`

Explanation

for ray `h_(1)`
`sin i=(12)/(20) rArr sin i=(3)/(5) rArr sin i=0.6 rArr i=37^(@)`
applying snell's law of refraction
`mu_(g)sin i =mu_(a) sinr rArr 1.6 sin i =sin r`
`sin r=0.96 rArrr=74^(@)`
`delta=r-i rArr delta=74^(@)-37^(@)`
`delta=37^(@) rArr tandelta=(12)/(x_(1))`
`tan 37^(@) =(12)/(x_(1))` `rArr x_(1)=(12)/(tan37^(@))`
`x_(1)=16cm`
for ray `h_(2)`

`sin i=(0.5)/(20) rArr sin i=(1)/(40) rArr i=(1)/(40)` rad applying snell's law of refraction
`mu_(g) sin i=mu_(a) sin r rArr 1.6 i=mu_(a)r rArr =1.6xx(1)/(40) rArr r=(1)/(25)`
`delta=r-i rArr delta=(1)/(25)-(1)/(40) rArr delta=(3)/(200)`
`tan delta=(3)/(200) rArr (0.5)/(x_(2))=(3)/(200)`
`x_(2)=(100)/(3)cm=33.3cm`
` Deltax=(x_(2)+4)-x_(1)` ltbegt `Deltax=(33.3+4)-16`
`Deltax=21.3 cm`