The powers of the two convex lenses are +2D and +4D respectively.
- Which of them is thicker? Give reason.
- Calculate the focal length of each lens.
Solution
1.Ans:
In general, a lens with higher power is thinner than a lens with lower power. Therefore, the +2D lens is thicker than the +4D lens, as the +4D lens has a shorter focal length and is designed to be more compact.
2.Ans:
To calculate the focal length of each lens we use the formula:
\(\rm P \) = $\frac{1}{f}$
where \(\rm P\) = Power of lens
and, \(\rm f\) = focal length of lens
For +2D:
\(\rm P \) = $\frac{1}{f}$
\(\rm or,\) \(\rm +2 \) = $\frac{1}{f}$
\(\rm or,\) \(\rm f \) = $\frac{1}{2}$
\(\rm or,\) \(\rm P \) = \(\rm 0.5\)
Hence, for lens with power +2D focal length is 0.5 m or 50 cm.
For +4D:
\(\rm P \) = $\frac{1}{f}$
\(\rm or,\) \(\rm +4 \) = $\frac{1}{f}$
\(\rm or,\) \(\rm f \) = $\frac{1}{4}$
\(\rm or,\) \(\rm P \) = \(\rm 0.25\)
Hence, for lens with power +4D focal length is 0.25 m or 25 cm.