Question 78: Ray Optics

Question

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $$25 \mathrm{D}$$. Focal length of each of the convex lens is:

Accepted Answer

When we have a combination of identical lenses in contact, the effective power ($$P_{	ext{eff}}$$) of the combination can be calculated as the sum of the powers of all the individual lenses. This is because the lenses are in direct contact, and their powers effectively add up.
Given that the effective power of a combination of 5 identical convex lenses is $$25 \mathrm{D}$$, we can use the formula for the effective power of the combination:
$$P_{	ext{eff}} = nP$$
where:
$P_{	ext{eff}}$ is the effective power of the combination,
$n$ is the number of lenses, and
$P$ is the power of each individual lens.
Given $n = 5$ and $P_{	ext{eff}} = 25 \mathrm{D}$, we can solve for $P$, the power of each lens:
$$25 \mathrm{D} = 5P$$
Dividing both sides by 5:
$$P = \frac{25 \mathrm{D}}{5} = 5 \mathrm{D}$$
The power of a lens ($P$) is related to its focal length ($f$) by the equation:
$$P = \frac{1}{f}$$
where $P$ is in diopters (D) and $f$ is in meters. Thus:
$$5 \mathrm{D} = \frac{1}{f}$$
Solving for $f$ gives:
$$f = \frac{1}{5} 	ext{ meters} = \frac{1}{5} 	imes 100 	ext{ cm} = 20 	ext{ cm}$$
Therefore, the focal length of each of the convex lenses is 20 cm. So, the correct answer is
Option B: 20 cm
.

Answer

50 cm

Answer

20 cm

Answer

25 cm

Answer

500 cm

Ray Optics

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $25 \mathrm{D}$. Focal length of each of the convex lens is:

Choose the correct answer: