Question

Rays from the sun converge at a point 25 cm behind a convex lens. The distance at which an object be placed in front of the lens to get a virtual image, is:

• A. 20 cm
• B. 40 cm
• C. 50 cm
• D. More than 50 cm

Hint:

Convex lens gives virtual image only when object is within focal length.

Answer 1

The Correct Option is A

To solve this problem, we need to understand the behavior of a convex lens and apply the lens formula. When rays from the sun converge at a point behind a convex lens, that point is the focal point of the lens. This gives us the focal length (\(f\)) of the lens.

Given:

• Focal length of the lens, \(f = 25\,\text{cm}\) (since the rays converge at the focal point).

We need to find the distance at which an object should be placed in front of the lens to get a virtual image. For a convex lens, a virtual image is formed when the object is placed within the focal length. This means the object distance (\(u\)) must be less than the focal length, so \(u < f\).

The lens formula is given by:

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

Where:

• \(f\) is the focal length of the lens.
• \(v\) is the image distance.
• \(u\) is the object distance. (We consider \(u\) negative for object distance in lens formula calculations).

Since we want a virtual image, the image will be formed on the same side as the object, which means \(v\) will be negative. Let's calculate \(u\) using \(v = -25\,\text{cm}\). However, primarily we affirm that to obtain a virtual image, \(|u|\) must be less than the focal length. Thus, placing an object at \(20\,\text{cm}\) (i.e., less than \(25\,\text{cm}\)) will satisfy this condition.

Thus, the correct answer is:

• 20 cm