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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.
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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