Question

A convex lens has a focal length of 20 cm. An object is placed 30 cm in front of the lens. What is the image distance from the lens?

• A. \( 12 \, \text{cm} \)
• B. \( 60 \, \text{cm} \)
• C. \( 15 \, \text{cm} \)
• D. \( 30 \, \text{cm} \)

Hint:

In lens problems, follow the sign convention carefully: object distance \( u \) is negative for real objects, and focal length \( f \) is positive for convex lenses. A positive image distance \( v \) indicates a real image.

Answer 1

The Correct Option is B

To find the image distance for a convex lens, we use the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where: - \( f = 20 \, \text{cm} \) (focal length of the convex lens, positive for convex lens), - \( u = -30 \, \text{cm} \) (object distance, negative as the object is on the side of incident light), - \( v \) is the image distance (to be determined). Rearrange the lens formula to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \] Substitute the values: \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-30} \] \[ \frac{1}{v} = \frac{1}{20} - \frac{1}{30} \] Find a common denominator (LCM of 20 and 30 is 60): \[ \frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{3 - 2}{60} = \frac{1}{60} \] \[ v = 60 \, \text{cm} \] The positive value of \( v \) indicates that the image is formed on the opposite side of the lens from the object, which is consistent for a real image formed by a convex lens when the object is beyond the focal point. Thus, the image distance from the lens is \( 60 \, \text{cm} \).