Question

An object is placed at a distance of 10 cm from a concave mirror of focal length 15 cm. What is the image distance?

• A. \( 30 \, \text{cm} \)
• B. \( 20 \, \text{cm} \)
• C. \( 50 \, \text{cm} \)
• D. \( 60 \, \text{cm} \)

Hint:

Remember: For a concave mirror, the focal length is negative and the image distance can be positive or negative depending on the nature of the image.

Answer 1

The Correct Option is A

Step 1: Use the mirror formula
The mirror formula relates the object distance \( u \), the image distance \( v \), and the focal length \( f \): \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where: 
- \( f \) is the focal length, 
- \( v \) is the image distance, 
- \( u \) is the object distance. 
Step 2: Substitute the given values
Given: 
- Focal length \( f = -15 \, \text{cm} \) (for concave mirror, focal length is negative), 
- Object distance \( u = -10 \, \text{cm} \) (object is always placed on the same side as the incoming light). 
Substitute these values into the formula: \[ \frac{1}{-15} = \frac{1}{v} + \frac{1}{-10} \] \[ \frac{1}{v} = \frac{1}{-15} + \frac{1}{10} \] \[ \frac{1}{v} = \frac{-2 + 3}{30} \] \[ \frac{1}{v} = \frac{1}{30} \] \[ v = 30 \, \text{cm} \] 
Answer:
Therefore, the image distance is \( 30 \, \text{cm} \). So, the correct answer is option (1).