Optics 1 Question 13

13. A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated, just touches the rod. The magnification is ……

(1991, 1M)

Integer Answer Type Question

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Answer:

Correct Answer: 13. (1.5)

Solution:

  1. F= focus, C= centre of curvature

When the object lies between F and C, image is real, elongated and inverted. As one end of rod just touches its image, this end should lie at C. Because image of object at C is at C itself.

Let P be the image of other end of rodP.

For P

u=(2ff/3)=5f3

Applying the mirror formula :1v+1u=1f

 or 1v35f=1f1v=35f1f or v=5f2 or OP=5f2

Length of image of rod

CP=OPOC=5f22f=f2 Magnification =f/2f/3=1.5

Here, negative sign implies that image is inverted.



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