BITSAT 2015
- Exam
- BITSAT
- Year
- 2015
- Subject
- Physics
- Chapter
- Ray Optics
BITSAT 2015 · Physics · Ray Optics
A planoconvex lens fits exactly into a planoconcave lens. Their...
A planoconvex lens fits exactly into a planoconcave lens. Their plane surface are parallel to each other. If the lenses are made of different materials of refractive indices and is the radius of curvature of the curved surface of the lenses, then focal length of combination is
Options
- A
- B
- C\frac{R}{2\left(\mu_{1}-\mu_{2}\right)}
- D\frac{R}{2-\left(\mu_{1}+\mu_{2}\right)}
Correct answer
A.
Step-by-step solution
If F be the equivalent focal length, then \begin{aligned} \frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}} \quad \frac{1}{F}= \left(\mu_{1}-1\\right)\left(\frac{1}{\infty}+\frac{1}{R}\right)\\ +\left(\mu_{2}-1\\right)\left(\frac{1}{-R}-\frac{1}{\infty}\right)=\frac{\mu_{1}-\mu_{2}}{R}\\ F=\frac{R}{\mu_{1}-\mu_{2}} \end{aligned}