Physics Ncert Solutions Class 12th Physics Class 12th Wave Optics

10.12 Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

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10.12 Newton's corpuscular theory of light states that when light corpuscles strike the interface of two media from a rarer (air) to a denser (water) medium, the particles experience forces of attraction normal to the surface. Hence, the normal component of velocity increases while the component along the surface remains unchanged.

Hence, we can write the expression:

$c sin ? i = v \sin ? r$ ……… (1)

Where, I = angle of incidence, r = angle of reflection, c = velocity of light in air and v = velocity of light in water

We have the relation for relative refractive index of water with respect to air is $? = \frac{v}{c}$

So from equation (1) we get

$\frac{v}{c}$ = $\frac{\sin ? i}{\sin ? r}$ = $?$

But $? > 1, v > c$ Th

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Hence, we can write the expression:

$c sin ? i = v \sin ? r$ ……… (1)

Where, I = angle of incidence, r = angle of reflection, c = velocity of light in air and v = velocity of light in water

We have the relation for relative refractive index of water with respect to air is $? = \frac{v}{c}$

So from equation (1) we get

$\frac{v}{c}$ = $\frac{\sin ? i}{\sin ? r}$ = $?$

But $? > 1, v > c$ This is not possible since the prediction is opposite to the experimental results of c > v. The wave picture of light is consistent with the experimental results.

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10.12 Newton's corpuscular theory of light states that when light corpuscles strike the interface of two media from a rarer (air) to a denser (water) medium, the particles experience forces of attraction normal to the surface. Hence, the normal component of velocity increases while the component along the surface remains unchanged.Hence, we can write the expression: <math> <mrow> <mrow> <mi mathvariant="normal">c sin</mi> </mrow> <mo>? </mo> <mrow> <mi>i</mi> </mrow> </mrow> <mo>=</mo> <mi>v</mi> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>r</mi> </mrow> </mrow> </math> ……… (1)Where, I = angle of incidence, r = angle of reflection, c = velocity of light in air and v = velocity of light in waterWe have the relation for relative refractive index of water with respect to air is <math> <mi>? </mi> <mo>=</mo> <mi> </mi> <mfrac> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </mfrac> </math> So from equation (1) we get <math><mfrac><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mi>c</mi></mrow></mrow></mfrac></math> = <math><mfrac><mrow><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>? </mo><mrow><mi>i</mi></mrow></mrow></mrow></mrow><mrow><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>? </mo><mrow><mi>r</mi></mrow></mrow></mrow></mrow></mfrac></math>= <math> <mi>? </mi> </math> But <math> <mi>? </mi> <mo>></mo> <mn>1</mn> <mo>, </mo> <mi> </mi> <mi>v</mi> <mo>></mo> <mi>c</mi> </math> This is not possible since the prediction is opposite to the experimental results of c > v. The wave picture of light is consistent with the experimental results.

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