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A ray of blue light passes from air into a transparent block as shown - Scottish Highers Physics - Question 13 - 2017

Question 13

A ray of blue light passes from air into a transparent block as shown. The speed of this light in the block is A 1.80 x 10^8 ms⁻¹ B 1.96 x 10^8 ms⁻¹ C 2.00 x 10^8 ... show full transcript

Worked Solution & Example Answer:A ray of blue light passes from air into a transparent block as shown - Scottish Highers Physics - Question 13 - 2017

Step 1

Determine the refraction angles

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Answer

Using Snell's Law: $n_1 imes ext{sin}( heta_1) = n_2 imes ext{sin}( heta_2)$ where,

$n_1$ (refractive index of air) = 1,
$heta_1$ (angle of incidence in air) = 30°,
$heta_2$ (angle of refraction in block) = 40°.

Plugging in the values: $1 imes ext{sin}(30°) = n_2 imes ext{sin}(40°)$ Solving for $n_2$ gives us the refractive index of the block.

Step 2

Calculate the refractive index of the block

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Answer

Using the known values: $ext{sin}(30°) = 0.5, ext{sin}(40°) \approx 0.6428$

So, $1 imes 0.5 = n_2 imes 0.6428$ $n_2 = \frac{0.5}{0.6428} \approx 0.778$

Step 3

Find the speed of light in the block

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Answer

The speed of light in a medium is given by: $v = \frac{c}{n}$ where,

$c$ (speed of light in a vacuum) = $3.00 \times 10^8$ ms⁻¹.

Substituting for $n$ : $v = \frac{3.00 \times 10^8}{1.29} \approx 2.33 \times 10^8 ext{ms}^{-1}$ Thus, the closest answer choice is D: $2.23 \times 10^8 ext{ ms}^{-1}$ .

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