JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Curved Surfaces

  • question_answer
    Two plano-convex lenses each of focal length 10 cm & refractive index \[\frac{3}{2}\] are placed as shown. In the space left, water \[\left( R.l=\frac{4}{3} \right)\] is filled. The whole arrangement is in air. The optical power of the system is (in diopters)

    A)  6.67

    B)  - 6.67

    C)  33.3

    D)  - 33.3

    Correct Answer: A

    Solution :

    Focal length of plano-convex lens is 10 cm
    \[\frac{1}{10}=\left( \frac{3}{2}-1 \right)\left( \frac{1}{\infty }-\frac{1}{-R} \right)\]
    \[\frac{1}{10}=\frac{1}{2}\times \frac{1}{R}\Rightarrow R=5cm\]
    Let focal length of water lens is \[{{f}_{w}}\]
    \[\frac{1}{{{f}_{w}}}=\left( \frac{4}{3}-1 \right)\left( \frac{1}{-5}-\frac{1}{5} \right)\]
    \[\Rightarrow \]   \[f=-\frac{15}{2}cm=-\frac{0.15m}{2}=-\frac{3}{40}m\]
    Optical powers of system
    \[P=\frac{1}{f}+\frac{1}{f}+\frac{1}{{{f}_{w}}}=\frac{1}{0.1}+\frac{1}{0.1}+\left( -\frac{40}{3} \right)=6.67D\]

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