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CBSE Class 10 Science Solved Question Paper 2013

Long Answer Type

41.
(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium with speed of light in vacuum.
(b) The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is 2 × 10⁸ ms⁻¹, find the speed of light in (i) air, (ii) water.

(a) Laws of refraction states that:

First law of refraction: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is known as Snell’s law.

Mathematically, we have

$sini over sinr space equals space n subscript a b end subscript$

Here, n_ab is the relative refractive index of medium a with respect to medium b.

Second law of refraction: The incident ray, the refracted ray, and the normal to the interface of two media at the point of incidence; all lie in the same plane.

If the light ray goes from medium 1 to 2 then the refractive index of medium 1 with respect to medium 2 is,

$straight n subscript 12 space equals space fraction numerator Speed straight space of straight space light straight space in straight space medium space 2 over denominator speed straight space of straight space light straight space in straight space medium space 1 end fraction equals straight v subscript 2 over straight v subscript 1$
where v₁ and v₂ are the speeds of light in medium 1 and 2 respectively.

Given,

Refractive index of water, n_w = 4/3, and

Refractive index of glass, n_g= 3/2

Speed of light in glass, v_g = 2×10⁸ m/s
i. $straight n subscript straight g over straight n subscript straight a equals v subscript a over v subscript g space$ where, n_ais the refractive index of light in air and v_a is the speed of light in air.

$space space space v subscript a space equals straight n subscript straight g over straight n subscript straight a cross times v subscript g equals fraction numerator bevelled italic 3 over italic 2 over denominator italic 1 end fraction cross times left parenthesis 2 cross times 10 to the power of italic 8 right parenthesis equals space 3 cross times 10 to the power of 8 space m divided by s$
is the required speed of light in air.

ii. Speed of light in water is given by,

$straight n subscript straight g over straight n subscript straight w space equals space v subscript w over v subscript g space comma space W h e r e space v subscript w space equals space S p e e d space o f space l i g h t space i n space w a t e r T h e r e f o r e comma space v subscript w space equals space n subscript g over n subscript w space cross times space v subscript g space equals space end subscript space fraction numerator 3 divided by 2 over denominator 4 divided by 3 end fraction space cross times space left parenthesis 2 space cross times space 10 to the power of 8 space end exponent right parenthesis space equals space 2.25 space cross times space 10 to the power of 8$

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42.

(a) A person cannot read newspaper placed nearer than 50 cm from his eyes. Name the defect of vision he is suffering from. Draw a ray diagram to illustrate this defect. List its two possible causes. Draw a ray diagram to show how this defect may be corrected using a lens of appropriate focal length.

(b) We see advertisements for eye donation on television or in newspapers. Write the importance of such advertisements.

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