A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be 2.0 cm within the plastic. What is the beetle's actual distance beneath the surface?

검증된 단계별 안내

Step 1: Identify the concept involved in the problem. This problem deals with the refraction of light and the apparent depth versus actual depth phenomenon. The apparent depth is the depth perceived by an observer due to the bending of light as it passes through a medium with a different refractive index.

Step 2: Write down the formula that relates apparent depth and actual depth. The formula is:

d_a = d_r / n

, where

d_a

is the apparent depth,

d_r

is the real (actual) depth, and

n

is the refractive index of the medium.

Step 3: Rearrange the formula to solve for the actual depth. The equation becomes:

d_r = d_a 	imes n

. This allows us to calculate the real depth using the apparent depth and the refractive index.

Step 4: Determine the refractive index of polystyrene plastic. The refractive index of polystyrene is approximately

n = 1.59

. This value will be used in the calculation.

Step 5: Substitute the given values into the formula. The apparent depth is

d_a = 2.0 \(\text{ cm}\)

, and the refractive index is

n = 1.59

. Multiply these values to find the actual depth:

d_r = 2.0 	imes 1.59

. Perform the multiplication to find the result.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Refraction of Light

Refraction is the bending of light as it passes from one medium to another with a different density. In this scenario, light travels from the polystyrene plastic to the air, causing the apparent position of the beetle to differ from its actual position. The degree of bending depends on the refractive indices of the two materials involved.

Refractive Index

The refractive index is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. For polystyrene, the refractive index is typically around 1.59, which affects how deep the beetle appears when viewed from outside the plastic.

Apparent Depth

Apparent depth refers to the perceived depth of an object submerged in a medium, which can differ from its actual depth due to refraction. The formula for calculating the apparent depth involves the actual depth and the refractive index of the medium. Understanding this concept is crucial for determining the true position of the beetle within the polystyrene.