Blog Posts
A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
By
1. Given Data
Using the Cartesian sign convention for a convex mirror:
- Object Size (h1): +4.5 cm
- Object Distance (u): -12 cm
- Focal Length (f): +15 cm (Convex mirror)
2. Image Location Calculation
Using the Mirror Formula:
1/f = 1/v + 1/u
Rearranging to solve for image distance (v):
1/v = 1/f - 1/u
Substituting the values:
- 1/v = 1/15 - 1/(-12)
- 1/v = 1/15 + 1/12
- 1/v = (4 + 5) / 60
- 1/v = 9 / 60
- v = 60 / 9
- v = +6.7 cm
Image Position (v) = 6.7 cm behind the mirror
3. Magnification and Size
Using the Magnification Formula (m):
m = -v / u
Substituting values:
- m = -(6.7) / (-12)
- m = +0.56
Now, finding the Image Height (h2):
- h2 = m × h1
- h2 = 0.56 × 4.5
- h2 = +2.5 cm
Final Conclusion
- Location: 6.7 cm behind the mirror.
- Nature: Virtual and Erect (indicated by the positive sign of v and m).
- Size: 2.5 cm (Diminished).
4. What happens if the needle is moved farther away?
Effect of increasing distance
As the needle is moved farther from the mirror (u increases), the image shifts towards the focus (F) behind the mirror. The size of the image will continue to decrease gradually, but it will always remain virtual and erect.
Post a Comment