Problems on Lenses

Physics

example

Image formation for lenses with one side silvered

A plano convex lens of focal length has its plane surface silvered. An object is placed from the lens on the convex side. The distance of the image from the lens is:

or,
or,
or,
Now, this image acts as the object for the lens.
So,

or,
or,

example

Image formation from compound lenses

A converging lens of focal length and diverging lens of focal length are kept apart with their principal axes coinciding. Where shall an object be placed to form an image at infinity?

Two cases are possible.
Case 1:
Final image is formed by the concave lens.
For concave lens ;

Now, serves as image distance for the convex lens.
So, ;


from converging lens.

Case 2:
Final image is formed by convex lens. 
So,;
for convex lens to form image at infinity 
So for the concave lens, the image distance is ;  


or, , i.e, from diverging lens.

example

Image formation by broken lenses

A point object O is placed at a distance from a convex lens (focal length ) cut into two halves each of which is displaced by perpendicular to the principal axis. What is the distance between the two images formed?


or,
or,
So,

or,

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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