Question

An object is kept on the principal axis of a concave mirror of focal length
12 cm. If the object is at a distance of 18 cm from the mirror, calculate the
image distance. Determine the nature of the image formed by calculating magnification produced by the mirror.​

Answer 1

The final image, formed by the combination, is coinciding with the object itself. This implies that the rays, from the object, are retracing their path, after refraction from the lens and reflection from the mirror. The (refracted) rays are, therefore, falling normally on the mirror. Thus the image of the convex lens should form at the center of curvature of the convex mirror.We first find the image distance of the convex lens using the lens formula

1/V - 1/(12) =10

1/V=1/10 - 1/12

=2/120 = 60

v=60cm[this is at the centre of curvature of the mirror]

Thus we get the radius of curvature as

v−d=R

60−10=R,

R=50cm

thus we get the focal length as f= R/2

=25cm

solution

Answer 2

Answer:

v= -36cm and m=-2

Explanation:

f = -12cm

u = -18 cm

v = ?

mirror formula,

1/v + 1/u = 1/f

1/v = 1/f - 1/u

1/v = 1/-12 - (1/-18)

= 1/-12 + 1/18

= -3+2/36. ( L C M )

1/v = -1/36

v = -36 cm

magnification,

m = -v/u

= -(-36)/-18

= +36/-18

m= -2

nature of image is real and inverted.