se the exact values you enter to make later calculations. A ray of light strikes
ID: 1438137 • Letter: S
Question
se the exact values you enter to make later calculations. A ray of light strikes a flat, 2.00-cm-thick block of glass (n = 1.33) at an angle of ? = 38.8° with respect to the normal (see figure below).
(a) Find the angle of refraction at the top surface and the angle of incidence at the bottom surface.
= ?°
(b) Find the refracted angle at the bottom surface.
=?°
(c) Find the lateral distance d by which the light beam is shifted.
=? cm
(d) Calculate the speed of light in the glass.
=? m/s
(e) Calculate the time required for the light to pass through the glass block.
= ?s
(f) Is the travel time through the block affected by the angle of incidence?(choose 1 from below)
Yes, a slightly larger angle will decrease the travel time
.Yes, a slightly larger angle will increase the travel time.
No
thankyou :D
2.00 cmExplanation / Answer
A. Snell's law
n1*sin A1 = n2*sin A2
refracted angle: A2 = arcsin((1*sin 38.8 deg)/1.33) = 28.10 deg
Since the second surface (labeled 2) is parallel to the first, the angle of incidence at the bottom surface is exactly the same as the refracted angle at the top surface following the theorem of geometry
A2 = A3 (Angle of incidence) = 28.10 deg
B. Again by snell's law
A4 = arcsin((1.5*sin 28.10 deg)/1.00) = 38.78 deg
C. Let L = 2.00 cm be the thickness of the glass. The angle of refraction at the first surface from Part (a) is A1 = 28.10 deg . Let h represent the distance from point a to c
h = L/cos A1 = 2/cos 28.10 deg = 2.27 cm
From the drawing above, note that angle alpha = A1 A2 = 38.8 28.10 = 10.7 deg and also that d represents the opposite side of the right-angle triangle defined by angle alpha with h being the hypotenuse of this triangle. Then
d = h*sin 10.7 deg = 2.27*sin 10.7 deg = 0.42 cm
D. Speed of light
v = c/ng = 3*10^8/1.33 = 2.25*10^8 m/sec
E. The time it will take the light beam to travel through the glass is therefore
t = h/v = 2.27*10^-2/(2.25*10^8) = 0.10088 ns
F.
If the angle of incidence A1 on the top surface is changed, the angle of refraction for that surface A2 will change and the path length h that the light beam takes will be modified base on the above equation for h. Since the value for h changes the time it takes for the light beam to travel through the glass will change based upon the equation above
Larger angle means vallue of h will increase which means travel time will increase.
Yes, a slightly larger angle will increase the travel time.
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