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Question

(a) An object is placed just outside the principal focus of concave mirror. Draw a ray diagram to show how the image is formed, and describe its size, position and nature. (b) If the object is moved further away from the mirror, what changes are there in the position and size of the image ? (c) An object is 24 cm away from a concave mirror and its image is 16 cm from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.

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Solution

(a)

image is real. inverted and magnified It is formed beyond the centre of curvature of the mirror.
(b) It the object is moved further away from the mirror. the image is formed nearer to the mirror and its size goes on decreasing.
(c)u = -24cm
v = -16cm
f = ?, R = ?, 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 negative 16 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style negative 24 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 5 over denominator 48 end fraction f space equals space minus 9.6 space c m
focal length = 9.6cm
Now we have,
R equals 2 f R space equals space 2 cross times negative 9.6 space equals space minus 19.2 space c m r a d i u s space o f space c u r v a t u r e space equals space minus 19.2 space c m
We know that,
m space equals negative v over u m equals negative fraction numerator negative 16 over denominator negative 24 end fraction m space equals space minus 0.667 M a g n i f i c a t i o n space equals space minus 0.667

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