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Question:

A 2.0 cm tall object is placed 15 cm in front of a concave mirror of focal length 10 cm. What is the size and nature of the image?

1.0 cm, real

4 cm, real

4 cm, virtual

None of these

Solution:

According to the new Cartesian sign convention,
Object distance, u = -15 cm
Focal length of the concave mirror, f = -10 cm
Height of the object, h₀ = 2 cm
According to the mirror formula,
1/v + 1/u = 1/f
=> 1/v = 1/f - 1/u = 1/-10 + 1/-15 = -1/10 - 1/15 = (-3 - 2)/30 = -5/30 = -1/6
or v = -6 cm
The image is formed at a distance of 6 cm from the mirror on the same side as the object. It is a real image.
Magnification of the mirror, m = -v/u = h₁/h₀
=> -(-6)/(-15) = h₁/2
=> h₁ = -4 cm
Negative sign shows that the image is inverted.
The image is real, inverted, of size 4 cm at a distance of 6 cm in front of the mirror.