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CBSE Class 12 Physics 2023 Outside Delhi Set 1 Paper

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Question : 21 of 35
Marks: +1, -0
In the given figure the radius of curvature of curved face in the plano-convex and the plano-concave lens is 15 cm1 5 \text{ cm} each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.
Focal length of plano-convex lens be f1f_1
  1f1  =(1.5−1)(  115−  1∞)\;\frac{1}{f_1}\;=(1.5-1) \left(\;\frac{1}{15}-\;\frac{1}{\infty}\right)
Or,  1f1  =  130\text{Or,}\quad \;\frac{1}{f_1}\;=\;\frac{1}{30}
∴ f1  =30 cm\therefore \ f_1\;=30 \text{ cm}
Focal length of plano-concave lens be f2f_2
  1f2  =(1.5−1)(  1∞−  115)\;\frac{1}{f_2}\;=(1.5-1) \left(\;\frac{1}{\infty}-\;\frac{1}{15}\right)
∴    f2  =−30 cm\therefore \;\; f_2\;=-30 \text{ cm}
since, parallel rays are incident on the plano convex lens it will form an image at a distance 30 cm30 \text{ cm} from the lens (since, focal length is 30 cm30 \text{ cm} ).
This image will act as an object for the plano concave lens.
Object distance =30−20=10 cm=30-20=10 \text{ cm}
Applying lens formula,
  1v2−  1u2  =  1f2\;\frac{1}{v_2}-\;\frac{1}{u_2}\;=\;\frac{1}{f_2}
   Or,       1v2−  110  =−  130\;\text{ Or, }\;\; \;\frac{1}{v_2}-\;\frac{1}{10}\;=-\;\frac{1}{30}
So, v2=15 cmv_2=15\text{ cm}
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