Question

A concave mirror has a focal length of 15 cm. An object is placed 30 cm from the mirror. What is the image distance?

• A. 30 cm
• B. 45 cm
• C. 60 cm
• D. 20 cm

Hint:

Remember: For a concave mirror, use the mirror formula \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \), where the object distance \( u \) is negative.

Answer 1

The Correct Option is C

Given: 
Focal length, \( f = 15 \, \text{cm} \) 
Object distance, \( u = -30 \, \text{cm} \) (negative for real object) 

Step 1: Mirror Formula The mirror formula is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where: - \( f \) is the focal length, - \( v \) is the image distance, - \( u \) is the object distance. 

Step 2: Solve for Image Distance \( v \) Substitute the given values into the mirror formula: \[ \frac{1}{15} = \frac{1}{v} + \frac{1}{-30} \] \[ \frac{1}{15} = \frac{1}{v} - \frac{1}{30} \] \[ \frac{1}{v} = \frac{1}{15} + \frac{1}{30} = \frac{2 + 1}{30} = \frac{3}{30} = \frac{1}{10} \] \[ v = 10 \, \text{cm} \] 

Answer: The correct answer is option (c): 60 cm.