JEE Physics 2024 Question with Solution

Given: Two biconvex lenses have focal lengths $f_1 = 10 \, \text{cm}$ and $f_2 = 15 \, \text{cm}$.

Find: The distance between the lenses.

From the solution, the required condition is that parallel rays entering the system pass through the first lens focus and emerge parallel after the second lens. For this arrangement, the separation is the sum of the focal lengths:

$$D = f_1 + f_2$$

Substituting the given values,

$$D = 10 \, \text{cm} + 15 \, \text{cm} = 25 \, \text{cm}$$

Therefore, the distance between the two lenses is $25 \, \text{cm}$. The correct option is C.

Given: Two biconvex lenses $L_1$ and $L_2$ have focal lengths $10 \, \text{cm}$ and $15 \, \text{cm}$, respectively.

Find: The distance between $L_1$ and $L_2$.

If the image formed by the first lens acts as the object for the second lens and the emergent rays are parallel, then the image produced by the first lens must lie at the first focal point of the second lens.

So, the lens separation must equal the sum of the focal lengths:

$$D = f_1 + f_2$$

Now substitute:

$$D = 10 + 15 = 25 \, \text{cm}$$

Hence, the required distance is $25 \, \text{cm}$.