An object 2cm high is placed at distance of 16cm from a concave mirror which produces a real image 3cm high (i) what is the focal length of mirror (ii) find position of image.
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Given O = 2cm
u = 16cm(-ve)
I = 3cm(-ve){Since image is real it is inverted)
⇒ -v/u = I / O
⇒ v = -1(I * u/o) = (-3cm * -16cm/2 cm) = 24 cm (-ve)
By relation 1/f = 1/u + 1/v
⇒1/f = 1/-16 + 1/-24
= 3 + 2/-48
=-5/48
⇒f = 48/5 (-ve) = 9.6 cm(-ve)
∵ C > u > f
⇒ Image formed is beyond C
u = 16cm(-ve)
I = 3cm(-ve){Since image is real it is inverted)
⇒ -v/u = I / O
⇒ v = -1(I * u/o) = (-3cm * -16cm/2 cm) = 24 cm (-ve)
By relation 1/f = 1/u + 1/v
⇒1/f = 1/-16 + 1/-24
= 3 + 2/-48
=-5/48
⇒f = 48/5 (-ve) = 9.6 cm(-ve)
∵ C > u > f
⇒ Image formed is beyond C
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