Question

To get an image of magnification -1 on a screen using a lens of focal length 20 cm, the object distance must be:

• A. Less than 20 cm
• B. 30 cm
• C. 40 cm
• D. 80 cm

Hint:

The object distance in a lens equation is negative for virtual images and positive for real images. Here, we calculated using the fact that magnification is -1.

Answer 1

The Correct Option is C

To solve this, we use the lens formula: \[\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\] where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance. With magnification \( M = -1 \), and knowing \[M = \frac{v}{u}\] we get: \[v = -u\] Substitute \( v = -u \) into the lens formula: \[\frac{1}{f} = \frac{1}{-u} - \frac{1}{u} = -\frac{2}{u}\] Given \( f = 20 \) cm: \[\frac{1}{20} = -\frac{2}{u}\] Solving for \( u \): \[u = -40 \, {cm}\] The object distance is 40 cm. The correct answer is option (3).