10.9 Light of wavelength 5000 Å falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

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Payal Gupta | Contributor-Level 10

5 months ago

10.9 Wave length of the incident light, $?$ = 5000 $* 10^{- 10}$ m

Speed of light, c = 3 $* 10^{8}$ m/s

Frequency of the incident light, $?$ = $\frac{c}{?}$ = $\frac{3 * 10^{8}}{5000 * 10^{- 10}}$ Hz= 6 $* 10^{14}$ Hz

The wavelength and frequency of incident ray will be same as of reflected ray. So the wavelength of the reflected ray will be 5000 Å and the frequency will be 6 $* 10^{14}$ Hz

When reflected ray is normal to the incident ray, the sum of incidence angle $? i$ and the reflected angle $? r$ will be 90 $°$

According to the law of reflection, the incidence angle and the reflected are same, i.e. $? i = ? r$

Hence, $? i + ? r$ = 2 $? i$ = 90 $°$

So $? i = ? r = 45 °$

Therefore, the angle of incidence for the given condition is $45 °$ .

10.9 Wave length of the incident light, <math> <mi>? </mi> </math> = 5000 <math> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>10</mn> </mrow> </mrow> </msup> </math> mSpeed of light, c = 3 <math> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>8</mn> </mrow> </mrow> </msup> </math> m/sFrequency of the incident light, <math><mi>? </mi></math> =  <math> <mfrac> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> <mrow> <mrow> <mi>? </mi> </mrow> </mrow> </mfrac> </math>  =<math><mfrac><mrow><mrow><mn>3</mn><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>5000</mn><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>10</mn></mrow></mrow></msup></mrow></mrow></mfrac></math> Hz= 6 <math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>14</mn></mrow></mrow></msup></math> HzThe wavelength and frequency of incident ray will be same as of reflected ray. So the wavelength of the reflected ray will be 5000 Å and the frequency will be 6 <math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>14</mn></mrow></mrow></msup></math> HzWhen reflected ray is normal to the incident ray, the sum of incidence angle <math> <mi>? </mi> <mi>i</mi> </math> and the reflected angle <math> <mi>? </mi> <mi>r</mi> <mi> </mi> </math> will be 90 <math> <mo>°</mo> </math> According to the law of reflection, the incidence angle and the reflected are same, i.e. <math> <mi>? </mi> <mi>i</mi> <mo>=</mo> <mi> </mi> <mi>? </mi> <mi>r</mi> </math> Hence, <math> <mi>? </mi> <mi>i</mi> <mo>+</mo> <mi> </mi> <mi>? </mi> <mi>r</mi> </math> = 2 <math> <mi>? </mi> <mi>i</mi> </math> = 90 <math> <mo>°</mo> </math> So<math><mi>? </mi><mi>i</mi><mo>=</mo><mi></mi><mi>? </mi><mi>r</mi><mo>=</mo><mn>45</mn><mo>°</mo></math>Therefore, the angle of incidence for the given condition is <math> <mn>45</mn> <mo>°</mo> </math> .

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10.9 Light of wavelength 5000 Å falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

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