IIT JEE Advanced 2010 Paper 2

Let V1 be the image distance from the lens.

Lens formula is

1

v

−

1

u

=

1

f

That is,

1

v1

−

1

−30

=

1

15

Therefore, v1 = 30 cm. For a plane mirror, the object distance is 20 cm. Therefore,
Image distance = 20 cm (Image I2)
Final image I3 is formed after refraction from the lens for which I2 acts as an object. The distance of I2 from the lens is 10 cm.
Therefore,

1

v3

−110 =

1

15

⇒

1

v3

=

1

10

+

1

15

=

5

30

⇒ v3 = 6 cm.
The image is real and at a distance 10 + 6 = 16 cm.