Question

A bulb is located on a wall. Its image is to be obtained on a parallel wall with the help of convex lens. If the distance between parallel walls is 'd' then required focal length of lens placed in between the walls is : -

• A. only $\frac{d}{4}$
• B. only $\frac{d}{2}$
• C. more than $\frac{d}{4}$ but less than $\frac{d}{2}$
• D. less than $\frac{d}{4}$

Answer 1

The Correct Option is B

To solve this problem, we need to use the lens formula and the concept of image formation by a lens. The bulb is located on one wall, and its image needs to be formed on a parallel wall across a distance d. We are to find the focal length f of the convex lens placed between the walls.

The lens formula is given by:

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

Where:

• u = Object distance from the lens
• v = Image distance from the lens
• f = Focal length of the lens

Given that the object and the image are on two parallel walls separated by distance d, we have:

u + v = d

We need to find f such that both these conditions are satisfied. By substituting v = d - u in the lens formula, we get:

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

Solving for the minimum focal length, we use the condition where object and image distances are equal, u = v = \frac{d}{2}:

Therefore, substituting back into the equation:

u = \frac{d}{2} and v = \frac{d}{2}

Now the focal length f is:

\frac{1}{f} = \frac{1}{\frac{d}{2}} - \frac{1}{\frac{d}{2}} = \frac{1}{\frac{d}{2}}

Which simplifies to:

f = \frac{d}{2}

Thus, the focal length of the lens needed to form an image of the bulb on the opposite parallel wall is \frac{d}{2}.

Therefore, the correct answer is:

only \frac{d}{2}