Light of wavelength =560.0 nm enters a block of clear plastic from air at an incident angle of θ

step 1 First, calculating the wavelength of light in plastic. So here I can write the value of lambda 2

Light of wavelength =560.0 nm enters a block of clear...

Light of wavelength $=560.0 \mathrm{nm}$ enters a block of clear plastic from air at an incident angle of $\theta_{\mathrm{i}}=36.1^{\circ}$ with respect to the normal. The angle of refraction is $\theta_{\mathrm{r}}=21.7^{\circ} .$ What is the speed of the light inside the plastic? a) $1.16 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$ c) $1.67 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$ e) $3.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$ b) $1.31 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$ d) $1.88 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$

Light of wavelength $=560.0 \mathrm{nm}$ enters a block of clear plastic from air at an incident angle of $\theta_{\mathrm{i}}=36.1^{\circ}$ with respect to the normal. The angle of refraction is $\theta_{\mathrm{r}}=21.7^{\circ} .$ What is the speed of the light inside the plastic?
a) $1.16 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
c) $1.67 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
e) $3.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
b) $1.31 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$
d) $1.88 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$

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Key Concepts

Snell's Law

Snell's Law is a fundamental principle in optics that relates the incident and refracted angles when light passes between two media with different refractive indices. It states that the product of the refractive index of the first medium and the sine of the incident angle is equal to the product of the refractive index of the second medium and the sine of the refracted angle. This law is essential for determining the bending of light at an interface.

Index of Refraction

The index of refraction is a dimensionless number that describes how much light slows down in a medium relative to its speed in a vacuum. It is calculated as the ratio of the speed of light in vacuum to the speed of light in the medium. This concept is central to understanding optical phenomena, as it directly influences the amount by which light is bent or refracted when entering a new medium.

Speed of Light in a Medium

The speed of light in a medium is determined by dividing the speed of light in vacuum by the medium's index of refraction. This concept illustrates how light propagates differently in various materials and is critical for solving problems where the change in speed results in refraction, such as when light transitions from air into plastic.

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