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A ray of monochromatic light passes from air into a block of glass as shown - Scottish Highers Physics - Question 14 - 2018

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A ray of monochromatic light passes from air into a block of glass as shown. The wavelength of this light in air is $6.30 \times 10^{-7}$ m. The refractive index of... show full transcript

Worked Solution & Example Answer:A ray of monochromatic light passes from air into a block of glass as shown - Scottish Highers Physics - Question 14 - 2018

Step 1

Calculate the frequency of light in air

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Answer

The frequency of light can be calculated using the formula:

f=cλf = \frac{c}{\lambda}

where:

  • ff is the frequency,
  • cc is the speed of light in a vacuum (3×1083 \times 10^8 m/s), and
  • λ\lambda is the wavelength in air (6.30×1076.30 \times 10^{-7} m).

Plugging in the values:

fair=3×1086.30×1074.76×1014 Hzf_{air} = \frac{3 \times 10^8}{6.30 \times 10^{-7}} \approx 4.76 \times 10^{14} \text{ Hz}

Step 2

Calculate the frequency in glass

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Answer

To find the frequency of light in the glass, we use the fact that frequency remains constant when light passes from one medium to another:

fglass=fairf_{glass} = f_{air}

Given that the refractive index (nn) is 1.501.50, the relationship between the speed of light in air (cc) and the speed of light in glass (vv) is given by:

v=cnv = \frac{c}{n}

Calculating the speed of light in glass, we find:

v=3×1081.50=2×108 m/sv = \frac{3 \times 10^8}{1.50} = 2 \times 10^8 \text{ m/s}

Therefore, the frequency in glass remains:

fglass=fair=4.76×1014 Hzf_{glass} = f_{air} = 4.76 \times 10^{14} \text{ Hz}

Matching this with the provided options, we find that option D) 4.76×10104.76 \times 10^{10} Hz is most likely a typographical error where the correct answer should have been 4.76×10144.76 \times 10^{14} Hz. Thus, the answer selected from the list is D.

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