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

We use the lens formula to solve this problem: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance. For magnification \( M = -1 \), we know that magnification is also given by the formula: \[ M = \frac{v}{u} \] Thus, for \( M = -1 \), we have: \[ v = -u \] Now, substitute \( v = -u \) into the lens formula: \[ \frac{1}{f} = \frac{1}{-u} - \frac{1}{u} = -\frac{2}{u} \] Given \( f = 20 \) cm, we substitute into the equation: \[ \frac{1}{20} = -\frac{2}{u} \] Solving for \( u \): \[ u = -40 \, {cm} \] Therefore, the object distance is 40 cm. Hence, the correct answer is option (3).