A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls. (a) A ray of monochromatic light passes through the glass prism and exits the plastic tank at point R, as shown. The refractive index of the glass for this light is 1.47. Calculate angle θ. (b) Calculate the critical angle of the glass for this light. (c) The plastic tank is now filled with vegetable oil. The refractive index of the vegetable oil for this light is 1.47. State at which point, P, Q, R, S, or T, the ray of light will now leave the plastic tank. Justify your answer.

Scottish Highers Physics Refraction of Light: A triangular prism of borosilica

A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls - Scottish Highers Physics - Question 11 - 2022

Question 11

A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls. (a) A ray of monochromatic light passes through the glass prism and e... show full transcript

Worked Solution & Example Answer:A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls - Scottish Highers Physics - Question 11 - 2022

Step 1

Calculate angle θ.

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Answer

To find angle θ, we use Snell's Law:

$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

Here, for air, the refractive index $n_1 = 1$ and for borosilicate glass, $n_2 = 1.47$ .

Let $heta_1 = 37°$ and $heta_2 = θ$ .

Substituting the values: $1 \cdot \sin(37°) = 1.47 \cdot \sin(θ)$

Calculating: $\sin(θ) = \frac{\sin(37°)}{1.47}$

Using a calculator, we find:

$θ \approx 26.2°$ .

Step 2

Calculate the critical angle of the glass for this light.

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Answer

The critical angle, $θ_c$ , can be calculated using:

$\sin(θ_c) = \frac{n_2}{n_1}$

Where $n_1 = 1$ (air) and $n_2 = 1.47$ (glass).

Thus: $\sin(θ_c) = \frac{1.47}{1}$

This yields: $θ_c \approx 42.9°.$

Step 3

State at which point, P, Q, R, S, or T, the ray of light will now leave the plastic tank. Justify your answer.

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Answer

The ray of light will leave the plastic tank at point P. This is because the refractive index of the vegetable oil is the same as that of the glass, hence there will be no refraction or change in speed/wavelength at this interface.

A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls - Scottish Highers Physics - Question 11 - 2022

Worked Solution & Example Answer:A triangular prism of borosilicate glass is placed inside a tank that has clear plastic walls - Scottish Highers Physics - Question 11 - 2022

Calculate angle θ.

Calculate the critical angle of the glass for this light.

State at which point, P, Q, R, S, or T, the ray of light will now leave the plastic tank. Justify your answer.

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