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1.6 is a refractive index of plano-convex lens, then the radius of curvature of the curved surface is 60 cm. The focal length of the lens is………….. cm
$ here , {1 \over f } = (1.6 -1) \left( {1 \over 60 } - {1 \over \infty} \right) = {1 \over 100} $ $ \therefore f = 100 cm $
One convex lens and one concave lens placed is contact with each other. If the ratio of their power is 2/3 and focal length of the combination is 30 cm, then individual focal lengths are
$ here, { P_1 \over P_2 } = {2 \over 3 } $ $ \therefore {f_2 \over f_1} ={2 \over 3} $ $ \therefore f_2 = { 2 f_1 \over 3} .....(1) $ $ Now, {1 \over 30} = { -1 \over f_1} + { 1 \over {2f_1 \over 3} } $ $ \therefore f_1 = -15 cm \;and f_2 = 10 cm $
A thin prism of $ 3 ^\circ $ , angle made from glass of refractive index 1.5 is combined with another thin prism made from glass of refractive index 1.3 to produce dispersion without deveation. what is the angle of Prism of second prism.
$ here, (n_1 -1 ) A_1 + (n_2 - 1 )A_2 = 0 $ $ \therefore 0.5 A_1 + 0.3 A_2 = 0 $ $ \therefore A_2 = { -1.5 \over 0.3} = -5 ^\circ $
If a ray of light is incident on a plane mirror at an angle of $ 30 ^\circ $ then deviation produced by a plane mirror is_ ..........
$ here, 180 - 60 ^\circ = 120 ^\circ $
The frequency of a light wave in a material is $ 4 \times 10 ^ {14} Hz $ and wavelength is $ 5000 A ^\circ $ . The refractive index of material will be_ ...........$ ( take c = 3 \times 10^8 ms^{-1} )$
$ use , \nu = f \lambda \; and n = { c \over \upsilon } $
If the refractive index of a material of an equilateral Prism is $ \sqrt 3 $ , then angle of minimum deviation will be
For an equilateral prism, the angle of the prism (A) is 60°. The refractive index (n) is given as √3. The formula for the angle of minimum deviation (D) is: n = sin((A + D)/2) / sin(A/2). Plugging in the values, we get: √3 = sin((60 + D)/2) / sin(30). Solving this equation gives us the angle of minimum deviation (D) as 60°.
If the critical angle for total internal reflection from a medium to vacuum is $ 30 ^\circ $ then velocity of light in the medium is ____$ ms^{-1} $ (take $c = 3.8 \times 10^8 ms^{-1} )$
A ray of light passes from glass ( n =1.5 ) to medium (n = 1.60) The value of the critical angle of glass is _ _____
A double convex lens of focal length 6 cm is made of glass of refractive index 1.5, The radius of curvature of one surface is double than that of the other surface. The value of small radius of curvature is .
$ use , \therefore {1 \over f } = (n-1) \left( {1 \over R_1} + {1 \over R_2 } \right) take R_1 = R_1 , R_2 = -2R $ R = 4.5 cm
When a ray of light enters in a transparent medium of refractive index n, then it is observed that the angle of refraction is half of the angle of incidence. The value of angle of incidence will be_______
$ here , n = { sin \over sin r } = { sin (i) \over sin ({i \over 2} ) } = { 2 sin ({i \over 2 } ) . cos ({i \over 2} ) \over sin ({i \over 2 } ) } $ $ \therefore n = cos \left( { i \over 2 } \right) $ $ \therefore {n \over 2 } = cos \left( { i \over 2 } \right) $ $ \therefore i = 2 cos^{-1} \left( { n \over 2 } \right) $
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