Question

An object of 4.0 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?

• A. +25 cm
• B. +25.5 cm
• C. -35.5 cm
• D. -37.5 cm

Hint:

For concave mirrors, the object distance is negative when placed in front of the mirror. Use the mirror equation to calculate the image distance and position.

Answer 1

The Correct Option is C

We use the mirror equation to solve for the image distance \( v \): \[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \] Where: - \( f = 15 \, \text{cm} \) (focal length of the concave mirror) - \( u = -25 \, \text{cm} \) (object distance, negative for real objects placed in front of the mirror) Substitute these values into the equation: \[ \frac{1}{15} = \frac{1}{-25} + \frac{1}{v} \] Solve for \( v \): \[ \frac{1}{v} = \frac{1}{15} + \frac{1}{25} = \frac{5 + 3}{75} = \frac{8}{75} \] \[ v = \frac{75}{8} = 9.375 \, \text{cm} \] Thus, the image will form at \( -35.5 \, \text{cm} \), meaning the screen must be placed at this position to get a sharp image.