JEE Physics 2025 Question with Solution

Given: A convex lens with object distance $u$, image distance $v$, and focal length $f$, with $|u| > f$.

Find: The correct graph relating $u$ and $v$.

Using the lens formula:

$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$

Rearranging,

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

Hence,

$$v = \frac{fu}{u-f}$$

This is not a linear relation. It represents a hyperbolic or inverse-type relation between $u$ and $v$.

As $u$ varies for $|u| > f$, the denominator $u-f$ controls the rapid change in $v$, so the graph is an inverse curve rather than a straight line or a parabola.

Therefore, the correct option is B.

Given: The relation between object distance $u$ and image distance $v$ for a convex lens.

Find: Which of the four graphs correctly represents the variation when $|u| > f$.

The lens formula is:

$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$

Multiplying through and rearranging gives:

$$uv = f(u+v)$$

or

$$v = \frac{uf}{u-f}$$

This equation shows that $v$ depends on $u$ through a rational expression, so the graph is a rectangular-hyperbola-type curve.

Thus:

• it is not a straight line,
• it is not a decreasing branch of the wrong sense,
• it is not a U-shaped curve.

So the inverse graph shown in the second figure matches the required relation. Therefore, the correct option is B.