A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle `theta``=30degree` to the axis of the lens, as shown in the figure
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point `(x,y)` at which the image is formed are

Options

A. `(0,0)`
B. `(50-25sqrt3`25)`
C. `(25,25sqrt3)`
D. `((125)/(3),25sqrt3)`

Answer

C

Explanation

For lens `(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(-50)=(1)/(30)`
`:'` `v=75cm`
Therefore object distance for mirror is 25cm and object is virtual
For minor `(1)/(v)+(1)/(u)=(1)/(f)` `:'` `(1)/(v)+(1)/(v)+(1)/(25)=(1)/(50)` `:'` `v=-50cm`
The image I would have formed as shown had the mirror been straight. But here the mirror is tilted by `30degree`. Therefore the image will be tilted by `60degree` and will be formed at A.
Here MA`=50` `cos60degree``=25cm`
and I`A `=50` `sin60degree` `=25sqrt3`cm