Directions: In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
Two identical double convex lenses each of the focal length/are made of glass of\[\mu =1.5.\]If R is the radius of curvature of each of the four faces. Then: (1) the focal length of combination is half the radius of curvature of any of the four faces (2) the focal length of combination increases if the lenses are separated by a distance\[f\]and the new focal length is twice its focal length when the lenses are in contact (3) the focal length of combination decreases when the lenses are separated by a distance\[f\]and the new focal length is half its focal length when the lenses are in contact (4) none of the aboveA) 1 and 2 are correct
B) 2 and 3 are correct
C) 1 and 4 and correct
D) 1, 2 and 4 are correct
Correct Answer: A
Solution :
\[\frac{1}{f}=(\mu -1)\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}} \right)\] Or \[\frac{1}{f}=\frac{1}{2}\times \frac{2}{R}\] Or \[R=f\] \[\therefore \] \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}\] \[\therefore \] \[F=\left( \frac{F}{2} \right)\] \[\therefore \]Focal length of the combination\[\frac{f}{2}=\frac{R}{2}=\]half the radius of curvature.
You need to login to perform this action.
You will be redirected in
3 sec
