A mirror forms an image which is 30 cm from an object and twice its height.

(a) Where must the mirror be situated?

(b) What is the radius of curvature?

(c) Is the mirror convex or concave?

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Solution

Let the image formed is virtual and erect.
v - u = 30cm
m = 2
(a)

Mirror is situated at a distance of 10cm from object.

(b)
$v equals negative 2 u equals 20 c m 1 over v plus 1 over u equals 1 over f fraction numerator begin display style 1 end style over denominator begin display style 20 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style negative 10 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style f end style end fraction 1 over f equals fraction numerator negative 1 over denominator 20 end fraction f equals negative 20 c m R equals 2 f space equals space minus 40 c m$
Radius of curvature = 40cm

(c)Concave mirror (since sign of focus is negative)

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A mirror forms an image which is 30 cm from an object and twice its height. (a) Where must the mirror be situated? (b) What is the radius of curvature? (c) Is the mirror convex or concave?

Let the image formed is virtual and erect. v - u = 30cm m = 2 (a) Mirror is situated at a distance of 10cm from object. (b) Radius of curvature = 40cm (c)Concave mirror (since sign of focus is negative)

A mirror forms an image which is 30 cm from an object and twice its height.

(a) Where must the mirror be situated?

(b) What is the radius of curvature?

(c) Is the mirror convex or concave?