Physics Problem: Spherical Mirror – Image Location and Magnification
Question:
Problem 3: An object is placed 80 mm away from the vertex of a convex spherical mirror.
The mirror has a radius of curvature of 240 mm.
Calculate the location and magnification of the image.
Also, describe the image: Is it real or virtual? Where is it located? Is it upright or inverted? Enlarged or reduced?
Answer and Explanation:
Step 1: Given Data
- Object distance, p = 80 mm
- Radius of curvature, R = 240 mm
- For convex mirrors, focal length f = −R/2 = −120 mm
Step 2: Use Mirror Formula
1/p + 1/q = 1/f
Substitute the known values:
1/80 + 1/q = 1/−120
⇒ 1/q = −1/120 − 1/80 = −(1/120 + 1/80)
LCM = 240, so:
1/q = −(2 + 3)/240 = −5/240
⇒ q = −48 mm
⇒ 1/q = −1/120 − 1/80 = −(1/120 + 1/80)
LCM = 240, so:
1/q = −(2 + 3)/240 = −5/240
⇒ q = −48 mm
The image is located 48 mm behind the mirror (negative sign indicates a virtual image).
Step 3: Magnification
m = −q/p = −(−48)/80 = 0.6
This means the image is upright and reduced since |m| < 1.
Step 4: Image Description
- Type: Virtual
- Location: Behind the mirror
- Orientation: Upright
- Magnification: Reduced (0.6×)
🔹 Image Location (q): −48 mm (behind the mirror)
🔹 Magnification (m): 0.6
🔹 Image Type: Virtual, Upright, Reduced