Answer:
Given data:
Magnification, m = 2
Object distance, u = ?
Image distance, v = -15.0 cm (as the image is real and on the opposite side of the lens)
Using the lens formula:
1/f = 1/v - 1/u
Since the image is real, v is negative. Substituting the values:
1/f = 1/-15 - 1/u
Multiplying both sides by -15u, we get:
-15u/f = u - 15
Rearranging, we get:
15u/f = 15 + u
Taking the reciprocal of both sides, we get:
f/15 = (u+15)/15u
Simplifying, we get:
f = 15u/(u+15) ------ (1)
We also know that the magnification, m = -v/u, since the image is real.
Substituting the given values:
2 = -v/u
v = -2u
Substituting v in terms of u in equation (1), we get:
f = -30u/(u-15) ------ (2)
Equations (1) and (2) represent two equations in two variables (u and f). Solving them simultaneously gives:
u = 30 cm
f = 45 cm
The sign of f is positive, indicating a convex lens.
Therefore, the answers are:
(a) Object distance, u = 30 cm
(b) Focal length, f = 45 cm
(c) Type of lens, convex lens.