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Chapter 23: Problem 36

An insect is trapped inside a piece of amber \((n=1.546)\) Looking at the insect from directly above, it appears to be \(7.00 \mathrm{mm}\) below a smooth surface of the amber. How far below the surface is the insect?

Short Answer

Expert verified
Based on the given information and the calculations according to Snell's law, the actual depth of the insect below the surface of the amber is approximately 10.8 mm.

Step by step solution

01

Identify the given information

From the problem, we know the following data: - Refractive index of air (n₁) = 1 (approximately) - Refractive index of amber (n₂) = 1.546 - Apparent depth of the insect (dₐ) = 7.00 mm
02

Use Snell's Law

Snell's Law states that the product of the refractive index and the angle of incidence in one medium is equal to the product of the refractive index and the angle of refraction in the other medium. Mathematically, this is expressed as: n₁ * sinθ₁ = n₂ * sinθ₂ Since we are looking directly above the insect, the angle of incidence (θ₁) and angle of refraction (θ₂) are 0 degrees, making sinθ₁ = sinθ₂ = 0.
03

Calculate the actual depth

We can't make use of Snell's law since sinθ₁ = sinθ₂ = 0. Instead, we can make use of the formula for refraction at a plane surface: Actual depth (d) = Apparent depth (dₐ) * (n₂ / n₁) Plug in the known values: d = 7.00 mm * (1.546 / 1) d = 7.00 mm * 1.546
04

Compute the result

Calculate the actual depth of the insect: d ≈ 10.822 mm So, the actual depth of the insect below the surface of the amber is approximately 10.8 mm.

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Most popular questions from this chapter

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