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Katena32 [7]
3 years ago
12

Given a 45 45 90 prism with index of 1.5, immersed in air. The hypotenuse acts as the reflecting face by TIR. A ray of light ent

ers horizontal (perpendicular to one of the non- hypotenuse faces) hitting the hypotenuse at 45º and is reflected. If the original ray is now the center of a converging bundle of rays, converging toward the original intersection point on the hypotenuse, what full convergence angle (in air) is allowed, if TIR at the hypotenuse is to be preserved for the whole bundle of rays?
Physics
1 answer:
Genrish500 [490]3 years ago
5 0

Answer:

83.6°

Explanation:

For the ray to be totally internally reflected, at the boundary, the angle of refraction is 90. Using the law of refraction where

n₁sinθ₁ = n₂sinθ₂ where n₁ = refractive index of prism = 1.5, θ₁ = critical angle in prism, n₂ = refractive index of air = 1 and θ₂ = refractive angle = 90°.

So, substituting these values into the equation,

n₁sinθ₁ = n₂sinθ₂

1.5 × sinθ₁ = 1 × sin90

1.5 × sinθ₁  = 1

sinθ₁ = 1/1.5

sinθ₁ = 0.6667

θ₁  = sin*(0.6667)

θ₁  = 41.8°

So, for total internal reflection, an incidence angle of 41.8° is required. So, a full convergence angle of 2 × 41.8° = 83.6° is required for the whole bundle of rays.

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Once the crate in sample problem 4C is in motion, a horizontal force of 53 N keeps the crate moving with a constant velocity. Fi
liraira [26]

Answer: k = 5.4kg/m

where m is the mass of the crate.

Explanation:

The force of kinetic friction is described by the equation:

Ff = k*N

in the opposite direction in wich the object moves, where k is the coefficient of kinetic friction and N is the normal force, that is equal to the weight of the crate. N = m*g where m is the mass of the crate and g is the gravitational acceleration.

If the crate keeps moving with constant velocity, this means that the crate is not accelerating so there is no net force applied on the crate. Then the friction force should be equal in magnitude to the horizontal force of 53N (but with different sign)

then we have:

k*m*g =  53N

k*m = 53N/9.8m/s^2 = 5.4kg

k = 5.4kg/m

In the question we do not have the mass of the crate, so you must put the value in that equation to get the value of k.

5 0
3 years ago
Read 2 more answers
A playground is on the flat roof of a city school, 6.2m above the street below. The vertical wall of the building is h=7.30m hig
olya-2409 [2.1K]

Answer:

a. 18.13m/s

b. 0.84m

c. 2.4m

Explanation:

a. to find the speed at which the ball was lunched, we use the horizontal component.Since the point distance from the base of the ball is 24m and it takes 2.20 secs to reach the wall,we can say that

t=distance /speed

speed v_{x}=vcos\alpha=24/2.2=10.9m/s\\V=10.9/cos53^{0}\\V=18.13m/s

Hence the speed at which ball was lunched is 18.13m/s

b. from the equation

y=v_{y}t-\frac{1}{2}gt^{2}\\ v_{y}=18.13sin53=14.48m/s\\\\y=(14.48*2.2)-\frac{1}{2}9.8*2.2^{2}\\y=8.14m\\

the vertical distance at which the ball clears the wall is

y=8.14-7.3=0.84m

c. the time it takes the ball to reach the 6.2m vertically

6.2=14.47t-4.8t^{2}\\\\14.47t-4.8t^{2}-6.2=0\\\using\\t=-b±\frac{\sqrt{b^{2}-4ac} }{2a}\\ where \\a=-4.8, b=14.47t, c=6.2\\hence t=2.4secs

the horizontal distance covered at this speed is

y+24=(18.13cos53)2.4\\y=26.186-24\\y=2.12m

4 0
3 years ago
A snail crawls 300 cm in 1 hour. Calculate the snail's speed in each of the following units. A) cm/h B) cm/min C) m/h
Crazy boy [7]
A) 300cm/h
B)1 hr=60 min
300/60=5
5cm/min
C)1m=100cm
300/100=3
3m/h
7 0
3 years ago
A car traveling at 35 m/s starts to decelerate steadily. It comes to a complete stop in 5 seconds. What is its acceleration.
Pepsi [2]
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7 0
3 years ago
If a 0.15 kg ball falls and has a KE of 20 J just before striking the ground, from what height did it fall. A. 1.36m B. 3m C. 13
RUDIKE [14]
According to the conservation of mechanical energy, the kinetic energy just before the ball strikes the ground is equal to the potential energy just before it fell. 

Therefore, we can say KE = PE
We know that PE = m·g·h

Which means KE = m·g·h

We can solve for h:

h = KE / m·g
   = 20 / (0.15 · 9.8) 
   = 13.6m

The correct answer is: the ball has fallen from a height of 13.6m.

5 0
3 years ago
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