What is the focal length of a convex lens of focal length $30 \, cm$ in contact with a concave lens of focal length $20 \, cm$? Is the system a converging or a diverging lens? Ignore thickness of the lenses.
(N/A) Focal length of the convex lens,$f_{1} = 30 \, cm$.
Focal length of the concave lens,$f_{2} = -20 \, cm$.
Let the focal length of the system of lenses be $f$.
The equivalent focal length of a system of two thin lenses in contact is given by the formula:
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
Substituting the values:
$\frac{1}{f} = \frac{1}{30} + \frac{1}{-20} = \frac{2 - 3}{60} = -\frac{1}{60} \, cm^{-1}$.
Therefore,$f = -60 \, cm$.
The negative sign indicates that the system of lenses acts as a diverging lens.
Focal length of the concave lens,$f_{2} = -20 \, cm$.
Let the focal length of the system of lenses be $f$.
The equivalent focal length of a system of two thin lenses in contact is given by the formula:
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
Substituting the values:
$\frac{1}{f} = \frac{1}{30} + \frac{1}{-20} = \frac{2 - 3}{60} = -\frac{1}{60} \, cm^{-1}$.
Therefore,$f = -60 \, cm$.
The negative sign indicates that the system of lenses acts as a diverging lens.
Explore More
Similar Questions
$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both curved surfaces have the same radius of curvature $R = 14\, cm$. For this bi-convex lens,for an object distance of $40\, cm$,the image distance will be.....$ cm$
Difficult
View SolutionAssertion: Two convex lenses joined together cannot produce an achromatic combination.
Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.
Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.
In the figure shown here,what is the equivalent focal length (in $cm$) of the combination of lenses (Assume that all layers are thin)?
MediumNEET 2023
View SolutionThe power of an achromatic convergent lens combination consisting of two lenses is $+ 2D$. The power of the convex lens is $+ 5D$. The ratio of the dispersive power of the convex lens to the concave lens will be:
Medium
View SolutionFind the position of the image formed by the lens combination given in the figure.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo