Question

Q-3. The image of an object placed in front of a concave mirror of focal length 12 cm is
formed at a point which is 10 cm more distant from the mirror than the object. Find the
magnification



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Answer 1

Answer: m = + 1.5

Explanation:

Let, object distance be = u

∴ v = (u + 10) cm

f = - 12 cm

We know,

1/f = 1/u + 1/v

=> - 1/12 = 1/u + 1/(u + 10)

=> (2u + 10)/u(u + 10) = - 1/12

=> (2u + 10)/(u² + 10u) = - 1/12

=> - u² - 10u = 24u + 120

=> - u² - 34u - 120 = 0

=> u² + 34u + 120 = 0

=> u² + (30 + 4)u + 120 = 0

=> u² + 30u + 4u + 120 = 0

=> u(u + 30) + 4(u + 30) = 0

=> (u + 30)(u + 4) = 0

Therefore, u = - 30 cm or u = - 4 cm.

Similarly, v = - 20 cm or v = 6 cm.

But, we will take u = - 4 cm and v = 6 cm as it is mentioned that the image is 10 cm more distant from the mirror than the object, i.e., it lies in between P and F.

Now, m = - v/u

=> m = - (6)/(- 4) = 3/2 = + 1.5.