Question

A convex lens of 20 cm focal length forms a real image which is three times magnified. The distance of the object from the lens is:

a. 60 cm
b. 40 cm
c. 30 cm
d. 20 cm

Answer 1

The object is placed 20 cm away from a convex lens with a focal length of 20 cm to form a real image magnified three times. By using the lens formula and the magnification formula, we can calculate that the correct answer is option (d).

Step-by-step explanation:

The question asks to determine the distance of the object from a convex lens given that the lens forms a real image magnified three times, and the focal length of the lens is 20 cm. To solve this problem, we can use the lens formula and magnification formula.

Step-by-Step Solution

1. The lens formula is given by 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance.
2. Magnification (m) is given by the formula m = -di/do.
3. Since the image is magnified three times, m = 3. Hence we can write m = -di/do = 3.
4. By cross-multiplying, we can solve for di: do = -di/3.
5. Substituting the value of do in the lens formula, we get 1/f = 1/(-di/3) + 1/di.
6. With the focal length given as 20 cm, or f = 20 cm, we can write 1/20 = 1/(-di/3) + 1/di.
7. By solving the equation, we find that the image distance di is -60 cm (negative because it's a real image on the same side).
8. Therefore, the object distance do is 20 cm.

Thus, the object is 20 cm from the lens, which corresponds to option (d).