In Fig. 33-50 a , a beam of light in material 1 is incident on a boundary at an angle θ 1 = 40°. Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction n 3 of the third material. Figure 33-50 b gives the angle of refraction θ 3 in that material versus n 3 for a range of possible n 3 values. The vertical axis scale is set by θ 3 a = 30.0° and θ 3 b = 50.0°. (a) What is the index of refraction of material 1, or is the index impossible to calculate without more information? (b) What is the index of refraction of material 2, or is the index impossible to calculate without more information? (c) If θ 1 is changed to 70° and the index of refraction of material 3 is 2.4, what is θ 3 ? Figure 33-50 Problem 50.
In Fig. 33-50 a , a beam of light in material 1 is incident on a boundary at an angle θ 1 = 40°. Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction n 3 of the third material. Figure 33-50 b gives the angle of refraction θ 3 in that material versus n 3 for a range of possible n 3 values. The vertical axis scale is set by θ 3 a = 30.0° and θ 3 b = 50.0°. (a) What is the index of refraction of material 1, or is the index impossible to calculate without more information? (b) What is the index of refraction of material 2, or is the index impossible to calculate without more information? (c) If θ 1 is changed to 70° and the index of refraction of material 3 is 2.4, what is θ 3 ? Figure 33-50 Problem 50.
In Fig. 33-50a, a beam of light in material 1 is incident on a boundary at an angle θ1 = 40°. Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction n3 of the third material. Figure 33-50b gives the angle of refraction θ3 in that material versus n3 for a range of possible n3 values. The vertical axis scale is set by θ3a= 30.0° and θ3b = 50.0°. (a) What is the index of refraction of material 1, or is the index impossible to calculate without more information? (b) What is the index of refraction of material 2, or is the index impossible to calculate without more information? (c) If θ1 is changed to 70° and the index of refraction of material 3 is 2.4, what is θ3?
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
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