A curved mirror brings collimated light to focus at x = 20 cm. as shown in figure (1). Then it is filled with water n = 
(as shown in Fig. (2)) and illuminated through a pinhole in a white card. A sharp image will be formed on the card at what distance, X?
Text Solution
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From , we find that the focal length of the mirror is f a = 20 cm (in air).
Suppose the focal length is f b when the mirror is filled with water. When paraxial rays are refracted at a plane surface, the object distance y and the image distance y' are related by
y' = 
, where n and n' are the refractive indices of the two media. As now y = f a , n' = 1, n = 1.33, we have f b = y' = 
= 
= 15 cm. For a concave mirror, if the object distance is equal to the image distance then it is twice the focal length, i.e., X = 2f b = 30 cm.
where n and n' are the refractive indices of the two media. As now y = f a , n' = 1, n = 1.33, we have f b = y' = 
= 
= 15 cm. For a concave mirror, if the object distance is equal to the image distance then it is twice the focal length, i.e.,
X = 2f b = 30 cm.
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