A convex lens of focal length 20cm is placed coaxially with a convex mirror of radius of curvature 20cm. The two are kept 15 cm apart. A point object is placed 40cm in front of the convex lens.Find the position of the image formed by the combination .
u = -40 cm (to the left of the lens axes)
And, f = 20 cm (to the right of the lens axes)
From the lens formula, we have:
1/v - 1/u = 1/f
⇒ 1/v = 1/f + 1/u
⇒ 1/v = 1/20 + 1/( - 40 )
⇒ 1/v = (2 - 1)/40 = 1/ 40 ⇒ v = 40 cm
The positive sign shows that the image is formed to the right of the lens as shown in the following figure.
The image I1 is formed behind the mirror and hence acts as a virtual source for the mirror. The convex mirror forms the image I2, whose distance from the mirror can be calculated as:
1/ v + 1 /u = 1 /f
Here: u =25 cm
And , f = R/2 = 10 cm
⇒ 1/v = 1/f - 1/u
⇒ 1/v = 1/10 - 1/25
⇒ 1/v = (5 - 2)/ 50 = 3/ 50
⇒ v = 16 . 67 cm
Hence, the final image is formed at a distance of 16.67 cm from the convex mirror as shown in the following figure.