UPSEE Solved Model Paper 1

The incident ray OA Is refracted along BD by the lens.
Since the image coincides with the object, the refracted ray BD must retrace its path after reflection from the mirror, i.e. it falls normally on the mirror. Let C be the point on the axis where BD produced meets the axis.
It is clear that C is the centre of curvature of the mirror.
Also C is the image of the object O formed by the lens alone.
Thus
f = + 10 cm and u = -12 cm
The distance v of the image is obtained from the lens formula

1

v

−

1

u

=

1

f

Which gives v = -60 cm
Since x = 10 cm, R = v - x = 60 - 10 = 50 cm
Hence the focal length of the mirror

R

2

= 25 cm.