A 4.0cm tall object is placed perpendicular to the principal axis of a convex mirror of focal length 20cm. If the distance of the object from the lens is 30cm, find the position, nature and size of the image.
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Given
- Height of an object = 4 cm
- Focal length = 20 cm
- Lens used = convex
- Object Distance = -30 cm
To Find
- Object Distance
- Size of the image and it's magnification
Formulas Used
● 1/f = 1/v - 1/u [Lens Formula]
● Magnification = v/u
● Magnification = Image size/Object Size
Solution
- First we shall find the object Distance using the lens formula
✭ Object Distance :
→ 1/f = 1/v - 1/u
→ 1/20 = 1/v - 1/(-30)
→ 1/20 = 1/v + 1/30
→ 1/20 - 1/30 = 1/v
→ 3/60 - 2/60 = 1/v
→ 1/60 = 1/v
→ Image Distance = 60 cm
━━━━━━━━━━━━━━━━━━━━
✭ Magnification :
→ M = v/u
→ M = 60/(-30)
→ M = -2
✭ Image size :
→ M = Image Size/Object Size
→ -2 = Image Size/4
→ -2 × 4 = Image Size
→ Image Size = -8 cm
∴ The image is real inverted and magnification
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