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CBSE Class 12 Physics 2017 Outside Delhi Set 1 Paper

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Question : 15 of 26
Marks: +1, -0
(a) Monochromatic light of wavelength 589 nm589 \text{ nm} is incident from air on a water surface. If μ\mu for water is 1.33 , find the wavelength, frequency and speed of the refracted light.
(b) A double convex lens is made of a glass of refractive index 1.55 , with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm20 \text{ cm}.
Solution:  
(a) Calculation of wavelength, frequency and speed
(b) Lens Maker's Formula
Calculation of RR
(a) λ=589 nm1.33=442.8 nm\lambda = \frac{589 \text{ nm}}{1.33} = 442.8 \text{ nm}
Frequency v=3×108 ms−1589 nmv = \frac{3 \times 10^8 \text{ ms}^{-1}}{589 \text{ nm}}
=5.09×1012 Hz= 5.09 \times 10^{12} \text{ Hz}
Speed v=3×1081.33 m/sv = \frac{3 \times 10^8}{1.33} \text{ m/s} =2.25×108 m/s= 2.25 \times 10^8 \text{ m/s}
 (b) 1f=[μ2μ1−1][1R1−1R2]\text{ (b) } \frac{1}{f} = \left[ \frac{\mu_2}{\mu_1} - 1 \right] \left[ \frac{1}{R_1} - \frac{1}{R_2} \right]
∴120=[1.551−1]2R\therefore \frac{1}{20} = \left[ \frac{1.55}{1} - 1 \right] \frac{2}{R}
∴R=(20×1.10) cm=22 cm\therefore R = (20 \times 1.10) \text{ cm} = 22 \text{ cm}
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