A jeweller inspects the quality of a diamond. She uses a converging lens to produce a magnified image of the diamond. (a) Complete the ray diagram to show how a converging lens produces a magnified image of the object shown. (b) With the naked eye, the jeweller can detect a scratch that has a width of 0.1 mm or greater. The diamond has a scratch that is 10 µm wide. The jeweller holds the diamond 0.01 m from the converging lens and views the image of the diamond. Deduce, by calculation, whether the scratch is detectable by the jeweller using the lens. power of lens = 45 D (c) A ray of light enters the diamond along the normal at point Y as shown. The ray is incident at the diamond-air interface at X with an angle of incidence equal to 40º. Deduce whether the ray follows the path at X, as shown. speed of light in diamond = 1.25 × 10^8 ms^−1

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A jeweller inspects the quality of a diamond - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 2

Question 13

A jeweller inspects the quality of a diamond. She uses a converging lens to produce a magnified image of the diamond. (a) Complete the ray diagram to show how a con... show full transcript

Worked Solution & Example Answer:A jeweller inspects the quality of a diamond - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 2

Step 1

Complete the ray diagram to show how a converging lens produces a magnified image of the object shown.

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Answer

To complete the ray diagram, draw two rays originating from the object:

Draw a ray parallel to the principal axis, which refracts through the focus on the opposite side of the lens.
Draw a ray that passes through the center of the lens, which continues in a straight line. The point where these two rays converge indicates the location of the magnified image, which should be located on the same side of the lens as the object.

Step 2

Deduce, by calculation, whether the scratch is detectable by the jeweller using the lens.

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Answer

Given:

Width detectable = 0.1 mm = 100 µm
Width of scratch = 10 µm
Distance from lens to object (d_o) = 0.01 m

To find the magnification (M), we use the lens formula: $rac{1}{f} = rac{1}{d_o} + rac{1}{d_i}$ Where:

Power of lens (P) = 45 D implies $f = rac{1}{P} = rac{1}{45} m \approx 0.0222 m$
Plugging the values into the lens formula: $rac{1}{0.0222} = rac{1}{0.01} + rac{1}{d_i}$ Solving for $d_i$ results in the image distance. Calculate the magnification: $M = rac{d_i}{d_o}$ The size of the scratch in the image can be determined as: $10 ext{ µm} imes M$ If this result exceeds 100 µm, the scratch will be detectable.

Step 3

Deduce whether the ray follows the path at X as shown.

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Given the angle of incidence at point X is 40º and the speed of light in diamond is 1.25 × 10^8 ms^−1, first calculate the angle of refraction using Snell's Law: $n_1 imes ext{sin}( heta_1) = n_2 imes ext{sin}( heta_2)$ Where:

$n_1$ (air) is approximately 1.0,
$n_2$ (diamond) is calculated using the formula $n = rac{c}{v}$ , where $c$ is the speed of light in vacuum (~ $3 × 10^8 ms^{-1}$ ). This results in: $n_2 = rac{3 × 10^8}{1.25 × 10^8} = 2.4$ Finding the angle of refraction ( $heta_2$ ) will allow us to deduce the final path of the ray. If the angle of refraction is less than 90º and follows the predicted path shown in the diagram, then the ray follows that path.

A jeweller inspects the quality of a diamond - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 2

Worked Solution & Example Answer:A jeweller inspects the quality of a diamond - Edexcel - A-Level Physics - Question 13 - 2023 - Paper 2

Complete the ray diagram to show how a converging lens produces a magnified image of the object shown.

Deduce, by calculation, whether the scratch is detectable by the jeweller using the lens.

Deduce whether the ray follows the path at X as shown.

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