Question

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:

• A. 60 cm
• B. 40 cm
• C. 160 cm
• D. 100 cm

Hint:

For concave mirrors, the image distance is positive for real images and negative for virtual images. Use the mirror formula \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\) to find the image distance.

Answer 1

The Correct Option is C

Step 1: Understanding the Mirror Formula 
The mirror formula relates object distance \(u\), image distance \(v\), and the focal length \(f\) of the mirror: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Where: 
\(f = \frac{R}{2}\) is the focal length of the mirror and \(R\) is the radius of curvature. 
\(u\) is the object distance and \(v\) is the image distance. 
The radius of curvature \(R = 40 \, \text{cm}\), so the focal length is: \[ f = \frac{R}{2} = \frac{40}{2} = 20 \, \text{cm} \] 
Step 2: Finding the Image Distances 
For object A, placed at \(u_1 = 15 \, \text{cm}\), we use the mirror formula to find the image distance \(v_1\): \[ \frac{1}{f} = \frac{1}{v_1} + \frac{1}{u_1} \quad \Rightarrow \quad \frac{1}{20} = \frac{1}{v_1} + \frac{1}{15} \] Solving for \(v_1\): \[ \frac{1}{v_1} = \frac{1}{20} \frac{1}{15} = \frac{3 4}{60} = \frac{1}{60} \quad \Rightarrow \quad v_1 = 60 \, \text{cm} \] This indicates that the image is virtual and formed 60 cm behind the mirror. 
For object B, placed at \(u_2 = 25 \, \text{cm}\), we use the same formula to find the image distance \(v_2\): \[ \frac{1}{f} = \frac{1}{v_2} + \frac{1}{u_2} \quad \Rightarrow \quad \frac{1}{20} = \frac{1}{v_2} + \frac{1}{25} \] Solving for \(v_2\): \[ \frac{1}{v_2} = \frac{1}{20} \frac{1}{25} = \frac{5 4}{100} = \frac{1}{100} \quad \Rightarrow \quad v_2 = 100 \, \text{cm} \] 
This indicates that the image is real and formed 100 cm in front of the mirror. 
Step 3: Finding the Distance Between the Images 
The distance between the images is the difference in their image distances: \[ \text{Distance between images} = |v_2 v_1| = |100 (60)| = 100 + 60 = 160 \, \text{cm} \] 

Final Answer: The distance between the images formed by the mirror is \(160 \, \text{cm}\).