Two thin lenses have a combined power of +9 t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The equivalent power $P_{eq}$ of two thin lenses with powers $P_1$ and $P_2$ separated by a distance $d$ is given by the formula: $P_{eq} = P_1 +

Vedclass · Accepted Answer

$3, 6$

Vedclass · Answer

(B) The equivalent power $P_{eq}$ of two thin lenses with powers $P_1$ and $P_2$ separated by a distance $d$ is given by the formula: $P_{eq} = P_1 + P_2 - d P_1 P_2$.Given $P_1 + P_2 = 9 	ext{ D}$ and $d = 20 	ext{ cm} = 0.2 	ext{ m}$.Substituting the given values into the formula:$9 - (0.2) P_1 P_2 = \frac{27}{5} = 5.4$.Rearranging the terms to solve for $P_1 P_2$:$0.2 P_1 P_2 = 9 - 5.4 = 3.6$.$P_1 P_2 = \frac{3.6}{0.2} = 18$.We have a system of two equations: $P_1 + P_2 = 9$ and $P_1 P_2 = 18$.These are the roots of the quadratic equation $x^2 - 9x + 18 = 0$.Factoring the quadratic: $(x - 3)(x - 6) = 0$.Thus,the powers of the two lenses are $3 	ext{ D}$ and $6 	ext{ D}$.

Two thin lenses have a combined power of $+9 \text{ D}$. When they are separated by a distance of $20 \text{ cm}$,their equivalent power becomes $+\frac{27}{5} \text{ D}$. The power of both the lenses in dioptre are respectively:

Similar Questions

Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is $2:3$. The focal length of the system is $30 \ cm$. The focal lengths of individual lenses are

Three lenses of focal lengths $+10 \ cm, -10 \ cm$ and $+30 \ cm$ are placed at distances of $30 \ cm, 35 \ cm$ and $45 \ cm$ respectively from an object. The distance between the object and the final image formed is: (in $cm$)

Two lenses in contact made of materials with dispersive powers in the ratio $2 : 1$ behave as an achromatic lens of focal length $10\,cm$. The individual focal lengths of the lenses are:

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. If the effective focal length of the combination is $+60 \ cm$, then the focal lengths of the lenses should be:

Two lenses having focal lengths in the ratio $f_1:f_2 = 2:3$ are combined to produce no net dispersion. Find the ratio of the dispersive powers of the glasses used.

Vedclass Test Series

Exam Paper Generator

Online Exam Module