At what distance from a concave mirror of focal length 10 cm should an object be placed so that : (a) its real image is formed 20 cm from the mirror ? (b) its virtual image is formed 20 cm from the mirror ?

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Solution

(a)
f = −10 cm
v = −20 cm(real image)
now from the mirror formula
$1 over v space plus space 1 over u space equals space 1 over f fraction numerator 1 over denominator negative 20 end fraction space plus space 1 over u space equals space fraction numerator 1 over denominator negative 10 end fraction 1 over u space equals space fraction numerator 1 over denominator negative 10 end fraction space plus space 1 over 20 1 over u space equals space fraction numerator 1 over denominator negative 20 end fraction u space equals space minus 20 space c m$
Object must be placed at 20cm infront of mirror

(b)
f = −10 cm
v = 20 cm(virtual image)
now from the mirror formula
$1 over v space plus space 1 over u space equals space 1 over f 1 over 20 space plus space 1 over u space equals space fraction numerator 1 over denominator negative 10 end fraction 1 over u space equals space fraction numerator 1 over denominator negative 10 end fraction space plus space fraction numerator 1 over denominator negative 20 end fraction 1 over u space equals space fraction numerator negative 3 over denominator 20 end fraction u space equals space minus 20 over 3 space c m$
Object must be placed at 6.67cm infront of mirror.

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At what distance from a concave mirror of focal length 10 cm should an object be placed so that : (a) its real image is formed 20 cm from the mirror ? (b) its virtual image is formed 20 cm from the mirror ?

(a) f = −10 cm v = −20 cm(real image) now from the mirror formula Object must be placed at 20cm infront of mirror (b) f = −10 cm v = 20 cm(virtual image) now from the mirror formula Object must be placed at 6.67cm infront of mirror.