Effective Focal Length of Lens

Physics

example

Formation of image from a combination of lenses, mirrors and glass slabs

Example: A convex lens of focal length is held at a distance co-axially above a concave mirror of focal length . If the convex lens is replaced by a glass plate of thickness , refractive index and gives rise to an image coincident with itself, then what will be the value of ?

Solution:
When the  ray from O passes through the slab of refractive index  (), then there will be shift of point O to and then this point will act as source for the concave mirror.
Shift =
shift , i.e., the object will appear to look closer by .
Now as the final image is formed at a point O itself, so the ray from point will retrace its own path (i-e, should be at of concave mirror).
So,
 

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