A student obtained a sharp image of the grill of a window on a screen using a convex lens. For better results, the teacher suggests focusing of a distant tree instead of the grill. In what direction should the lens be moved for this purpose?

A
Away from the screen
B
Very far away from the screen
C
Behind the screen
D
Towards the screen

Solution:

A student obtained a sharp image of the grill of a window on a screen using a convex lens. For better results, the teacher suggests focusing of a distant tree instead of the grill. For this purpose the lens should move towards the screen.
We know that, lens formula is

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

For lens and grill system, object and image distances are u1 and v1 and that for lens and tree system are u2 and v2 respectively. And u1, u2 < 0
The lens formula for lens and grill system is

\frac{1}{v 1} - \frac{1}{u 1} = \frac{1}{f}

-------- (1)
And the lens formula for lens and tree system is

\frac{1}{v 2} - \frac{1}{u 2} = \frac{1}{f}

-------- (2)
As the RHS of both the equations is same, so

\frac{1}{v 1} - \frac{1}{u 1}

\frac{1}{v 2} - \frac{1}{u 2}

Or,

\frac{1}{v 2} - \frac{1}{v 1}

\frac{1}{u 1} - \frac{1}{u 2}

-------- (3)
We know that the tree is far away from the grill, so u1 < u2 or,

\frac{1}{u 1} > \frac{1}{u 2}

So, from (3), we get

\frac{1}{v 2} > \frac{1}{v 1}

or, v1 > v2
Hence, distance between lens and image gets reduced and hence lens is moved towards the screen.

A student obtained a sharp image of the grill of a window on a screen using a convex lens. For better results, the teacher suggests focusing of a distant tree instead of the grill. In what direction should the lens be moved for this purpose?

Solution:

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