Figure shown object`O`.Final image `I` isformed after two refraction and one refraction is also shown in figure .Find the length of mirror.(in cm).

Options

A. `10`
B. `15`
C. `20`
D. `25`

Answer

C

Explanation

`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
for reflraction at place surface
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(oo)`
`(mu_(2))/(v)=(mu_(1))/(u)`
` v=(mu_(2))/(mu_(1))xxu`
=`(1)/(4//3)xx(-33.25)`
`v=-25cm`
Image of object due to first refraction will act as object for mirror.Image due to reflected rays will acts as virtual object for refraction,
`(mu_(2))/(v)=(mu_(1))/(u) rArr u=(mu_(1))/(mu_(2))v`
` u=(1xx25)/(4//3) rArr u=(75)/(4)cm`
Applying mirror formula
`(1)/(v)+(1)/(u)=(1)/(f) rArr (1)/(-(15+75//4))+(1)/(-(15+25))=(1)/(f)`
`(1)/(f)=-[(4)/(135)+(1)/(40)] rArr (1)/(f)=-[(160+135)/(135xx40)]`
`f=-(135xx40)/(295) rArr f=-27xx(2)/(3)`
`f=-18cm`