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3 years ago

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Light traveling from water to a gemstone strikes the surface at an angle of 80.0º and has an angle of refraction of 15.2º . (a)

What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

1 answer:

7nadin3 [17]3 years ago

7 0

Answer:

a

The the speed of light in the gemstone is $v= 0.599*10^8 m/s$

b

The unreasonable thing about this is that the speed of ligth in the gemstone is too low

the speed is 19% of the speed of light which is very low

c

One main unreasonable or inconsistent factor is that the assumption that the differnce between the angle of incidence and angle of refraction is very large

Explanation:

From the question we are told that

The angle of incidence $i = 80^o$

The angle of refraction $r = 15.2^o$

From Snell's law we have ,

$n_1 sin \theta_1 = n_2 sin \theta_2$

Where $n_1$ is the refractive index of the first medium (water) with a constant value of $n_1 = 1..333$

$n_2$ is the refractive index of the second medium (gem stone)

$\theta_1$ is the angle between the beam and perpendicular surface of the first medium

$\theta_2$ is the angle between the beam an the perpendicular surface of the second medium

Making the $n_2$ the subject of the formula

$n_2 = n_1 \frac{sin \theta_1}{sin \theta_2}$

$= (1.333)(\frac{sin (80.0)}{sin 15.2} )$

$= 5.007$

Generally refractive index of a material is mathematically represented

$n = \frac{c}{v}$

Where c is the speed light

v is the speed of light observed in a medium

Making v the subject

$v = \frac{c}{n}$

substituting value for gem stone

$v = \frac{3.0*10^8}{5.007}$

$v= 0.599*10^8 m/s$

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Explanation:

a)

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2) Normal reaction (N): this is the reaction force exerted by the road on the bicyclist. This force acts vertically upward, and it balances the weight, so its magnitude is equal to the weight of the bicyclist, and its direction is opposite

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Here we can find the net force on the bicyclist by using Newton's second law of motion, which states that the net force acting on a body is equal to the product between the mass of the body and its acceleration:

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In this problem we have:

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We can write the net force acting on the bicyclist in the horizontal direction as the resultant of the two forces acting along this direction, so:

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In this problem we have:

$F_{net}=186 N$ is the net force (found in part b)

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