An object is placed 15 cm in front of a convex lens of focal length 25 cm. The image distance will be

Correct option is D

Correct Answer: (D) -37.5 cm

Explanation:

Using the lens formula:

​$$\frac 1f = \frac1v - \frac1u$$​​

Given:
f = +25 cm (convex lens)
u = -15 cm (Cartesian sign convention)

Substituting:
​$$\frac{1}{25} = \frac{1}{v} + \frac{1}{15}$$​

​$$\frac{1}{v} = \frac{1}{25} - \frac{1}{15}= \frac{3 - 5}{75}= -\frac{2}{75}$$​

v = -37.5 cm

Therefore, the image distance is -37.5 cm.
The image is virtual, erect, and magnified.

Information Booster:

• A convex lens forms a virtual and erect image when the object is placed between the optical centre and the focal point.
• The image formed in this case lies on the same side of the lens as the object, so the image distance is negative.
• The Cartesian sign convention assigns:
• Positive focal length to convex lenses.
• Negative object distance for objects placed to the left of the lens.

Additional Knowledge:

• (A) 17.5 cm: Incorrect; sign convention and calculation are not satisfied.
• (B) -9.37 cm: Incorrect value obtained from an erroneous calculation.
• (C) -10.0 cm: Incorrect; does not satisfy the lens formula.