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

Procedure:
1. Apply the mirror equation. The mirror equation establishes the relationship between object distance (\( u \)), image distance (\( v \)), and focal length (\( f \)): \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where:
- \( f \) represents the focal length.
- \( v \) denotes the image distance.
- \( u \) signifies the object distance.
2. Input the provided values.
Given:
- Focal length: \( f = -15 \, \text{cm} \) (focal length is negative for a concave mirror).
- Object distance: \( u = -10 \, \text{cm} \) (the object is always positioned on the same side as the incident light).
Substitute these values into the equation: \[ \frac{1}{-15} = \frac{1}{v} + \frac{1}{-10} \] Rearrange to solve for \( \frac{1}{v} \): \[ \frac{1}{v} = \frac{1}{-15} + \frac{1}{10} \] Perform the addition: \[ \frac{1}{v} = \frac{-2 + 3}{30} \] \[ \frac{1}{v} = \frac{1}{30} \] Solve for \( v \): \[ v = 30 \, \text{cm} \]
Conclusion:
The image distance is determined to be \( 30 \, \text{cm} \). Consequently, option (1) is the correct answer.