A concave mirror of radius of curvature 50 cm is used to form an image

A concave mirror of radius of curvature 50 cm is used to form an image of an object kept at a distance of 25 cm from the mirror on its principal axis. What will be the position of the image from the mirror ?

[amp_mcq option1=”At infinity” option2=”At 50 cm” option3=”At 25 cm” option4=”At 75 cm” correct=”option1″]

This question was previously asked in

UPSC CDS-2 – 2023

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The correct answer is A) At infinity.

The radius of curvature (R) of a concave mirror is 50 cm. The focal length (f) of a spherical mirror is half the radius of curvature, so f = R/2 = 50 cm / 2 = 25 cm. For a concave mirror, the focal length is considered negative in standard sign conventions when light comes from the left, so f = -25 cm. The object is kept at a distance of 25 cm from the mirror, which means the object distance (u) is -25 cm (object is real, placed on the left).
We use the mirror formula: 1/f = 1/v + 1/u, where v is the image distance.
Substituting the values: 1/(-25) = 1/v + 1/(-25)
-1/25 = 1/v – 1/25
1/v = -1/25 + 1/25
1/v = 0
This implies v = infinity.

When an object is placed at the focal point of a concave mirror, the rays of light from the object become parallel after reflection. Parallel rays meet at infinity, hence forming a real, inverted, and infinitely large image at infinity. This principle is used in devices like searchlights and headlights, where a light source is placed at the focus to produce a parallel beam of light.

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