PhysicsA transparent sphere of radius R and refractive index μ   is kept in the air. At what distance from the surface of the sphere should a point object be placed on the principal axis so as to form a real image at the same distance from the second surface of the sphere?

A transparent sphere of radius R and refractive index μ   is kept in the air. At what distance from the surface of the sphere should a point object be placed on the principal axis so as to form a real image at the same distance from the second surface of the sphere?


  1. A
  2. B
  3. C
  4. D
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    Solution:

    Concept- By maintaining the point object at a specific distance from the sphere's first surface in order to acquire its image at infinity (since the image is real) from the second surface, we may make a ray diagram.
    Given: A transparent sphere of radius R   and refractive index μ   is kept in the air.
    To find the distance from the surface of the sphere where a point should be placed so as to form a real image at the same distance from the other side of the sphere
     Using the equation,
    μ 2 v μ 1 u = μ 2 μ 1 R  
    For the refraction at the first surface of the sphere,
    (air to glass)
    μ 1 x = μ1 R  , Here x   is the distance of a point object from the sphere, as shown in above fig.
    1 x = μ1 R x= R μ1  
    Hence, the object should be placed this distance from the surface of the sphere in order to get a real image.
    Hence, option 3 is correct.
     
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