The size of an image of an object by a mirror having a focal length of 20 cm is observed to be reduced to ⅓ rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?
By BYJU'S Exam Prep
Updated on: September 13th, 2023
Given, focal length f = 20 cm
Magnification, m = 1/3
We have to find the distance of the object from the mirror.
Since the value of m is positive, the image is virtual and erect.
This implies that the mirror is a convex mirror.
We know, m = -(v/u)
1/3 = -v/u
v = -u/3
Using the mirror formula,
1/f = 1/v + 1/u
1/20 = 1/(-u/3) + 1/u
1/20 = -3/u + 1/u
1/20 = (-3+1)/u
1/20 = -2/u
u = -2(20)
u = -40 cm
Therefore, the required object distance is 40 cm.
Summary:
The size of an image of an object by a mirror having a focal length of 20 cm is observed to be reduced to ⅓ rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?
The size of an image of an object by a mirror having a focal length of 20 cm is observed to be reduced to ⅓ rd of its size. The object has been placed at a distance of 40 cm from the mirror. The mirror is convex and the image is virtual and erect.
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