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Question
A spherical mirror produces an image of magnification -1.0 on a screen placed at a distance of 30 cm from the pole of the mirror.
(i) Write the type of mirror in this case.
(ii) What is the focal length of the mirror ?
(iii) What is the nature of the image formed ?
(iv) Draw the ray diagram to show the image formation in this case.
Solution
Given :
m=-1 , v=-30 cm
We know that,
`m=-v/u`
`therefore -1=(30)/u`
`therefore u=-30`
(i) Since the magnification has a negative sign, the typa of mirror is a concave mirror
(ii) Using `1/f=1/v+1/u`, we get
`1/f=-1/30+(-1)/30`
`therefore 1/f=-2/30`
`therefore1/f=-1/15`
`=>f=-15` cm
∴ Focal length of the concave mirror is 15 cm
(iii) Since the magnitude of magnification is equal to 1 and the sign of magnification is negative, the image will be of the same size as the object, and its nature will be real and inverted.
(iv)
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