Question

A convex lens has a focal length of 20 cm. If an object is placed 30 cm from the lens, what is the image distance?

• A. 12 cm
• B. 15 cm
• C. 60 cm
• D. 90 cm

Hint:

Use the lens formula \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \), with the sign convention: \( f \) is positive for convex lenses, \( u \) is positive for real objects, and solve for \( v \).

Answer 1

The Correct Option is C

For a lens, use the lens formula: \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \] where \( f = 20 \, \text{cm} \) (focal length, positive for convex lens), \( u = 30 \, \text{cm} \) (object distance, positive as object is on the incident side). Solve for \( v \) (image distance): \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{20} - \frac{1}{30} = \frac{3 - 2}{60} = \frac{1}{60} \] \[ v = 60 \, \text{cm} \] Since \( v \) is positive, the image is formed 60 cm on the opposite side of the lens. The image distance is: \[ \boxed{60} \]