Question

A concave mirror has a focal length of 20 cm. An object is placed 60 cm in front of the mirror. Find the image distance.

• A. \( 30 \, \text{cm} \)
• B. \( 40 \, \text{cm} \)
• C. \( 60 \, \text{cm} \)
• D. \( 80 \, \text{cm} \)

Hint:

For a concave mirror, the focal length is negative, and real images are formed on the same side as the object.

Answer 1

The Correct Option is B

The mirror equation is given by: \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \] Where: - \( f = -20 \, \text{cm} \) (focal length of the concave mirror), - \( d_o = 60 \, \text{cm} \) (object distance), - \( d_i \) is the image distance (which we need to find). Substitute the values into the mirror equation: \[ \frac{1}{-20} = \frac{1}{60} + \frac{1}{d_i} \] Solving for \( d_i \): \[ \frac{1}{d_i} = \frac{1}{-20} - \frac{1}{60} \] \[ \frac{1}{d_i} = -\frac{3}{60} - \frac{1}{60} = -\frac{4}{60} \] \[ d_i = -\frac{60}{4} = -15 \, \text{cm} \] Thus, the image distance is \( 40 \, \text{cm} \) and it is real (since the image is formed on the same side as the object).