To find the focal length of a convex mirror , a student records the following data:
`{:("Object Pin","Convex Lens","Convex mirror","Image Pin"),(22.2 cm,32.2 cm,45.8 cm,71.2 cm):}`
The focal length of the convex lens is `f_(1)` and that of mirror is `f_(2)` . Then taking index correction to be negligibly small , `f_(1)` and `f_(2)` are close to :

Options

A. `{:(f_(1)=7.8cm,f_(2)=12.7cm):}`
B. `{:(f_(1)=12.7cm,f_(2)=7.8cm):}`
C. `{:(f_(1)=15.6cm,f_(2)=25.4cm):}`
D. `{:(f_(1)=7.8cm,f_(2)=25.4cm):}`

Answer

A

Explanation

The given figures shows the experimental set up to find the focal length of convex mirror using convex less

Fro lens
`mu_(1)=-(32.2-22.2)cm=-10cm`
`v_(1)=(71.2-32.2)cm=39cm`
`(1)/(f_(1))=(1)/(v_(1))-(1)/(u_(1))=(1)/(36)+(1)/(10)=(49)/(390)`
or `f_(1)=(390)/(49)cm=7.8cm`
For mirror `R=(71.2-45.8)cm=25.4cm`
or `f_(2)=(25.4)/(2)cm=12.7cm`