Physics Problem of the Day
Class XII — Ray Optics
A biology student uses a convex lens of focal length 20 cm to project the enlarged image of a microscopic specimen on a screen placed 60 cm from the lens. Determine:
- Position of the specimen
- Magnification produced
Given:
- Focal length, \(f = +20\ cm\)
- Image distance, \(v = +60\ cm\)
Detailed Solution
Using lens formula:
\[ \frac{1}{f} = \frac{1}{v} – \frac{1}{u} \]
Substituting values:
\[ \frac{1}{20} = \frac{1}{60} – \frac{1}{u} \]
Rearranging:
\[ \frac{1}{u} = \frac{1}{60} – \frac{1}{20} \]
\[ \frac{1}{u} = \frac{1-3}{60} = -\frac{2}{60} = -\frac{1}{30} \]
Therefore:
\[ u = -30\ cm \]
Hence the specimen is placed 30 cm in front of the lens.
Magnification
\[ m = \frac{v}{u} = \frac{60}{30} = 2 \]
Therefore magnification = 2.
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