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Question
A point object in the air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface with a refractive index of 1.5. If the radius of curvature of the surface is 20 cm, find the position of the image formed.
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Solution
We can use the mirror formula to find the position of the image formed by the concave spherical surface:
Since the object is placed symmetrically in front of the surface, we have:
u = 60 cm
Now, we can substitute these values into the formula:
`n_2/v - n_1/u = (n_2 - n_1)/R`
⇒ `1.5/v = (1.5 - 1)/(-20) + 1/(-60)`
⇒ `1.5/v = 0.5/(-20) - 1/60`
⇒ `1.5/v = -1/40 - 1/60`
⇒ `1.5/v = (-6 - 4)/240`
⇒ `1.5/v = (-10)/240`
⇒ `v = 240 xx 1.5/(-10) = -36`
Taking the reciprocal of both sides, we get:
`v = -36` cm
The negative sign indicates that the image is formed on the same side of the surface as the object, which means it is a virtual image. So, the image is formed 36 cm behind the concave spherical surface.
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