A pointsource of light is80.0cmbelow the surface of a body of water. Find the diameter of the circle at the surface through which light emerges from the water.

Short Answer

Expert verified

DiameterofCircle=1.82m

Step by step solution

01

Given

Depth of the source with respect to surface=80cm=0.8m

02

Understanding the concept

We can draw a ray diagram for the given problem. From the ray diagram, we can get the formula for the diameter of the circle. The value of critical angle can be found by using Snell’s law of refraction. Inserting it in that formula will give the diameter of the circle at the surface through which light emerges from the water.

03

Calculate the diameter of the circle at the surface through which light emerges from the water

Ray Diagram for the situation:

From the above diagram, we can say that

tan(90-θC)=DepthRadiusofCircleDiameterofCircle=2×radiusofcircleRadiusofCircle=DiameterofCircle2tan(90-θC)=DepthDiameterofCircle2

cotθC=DepthDiameterofCircle2tanθC=DiameterofCircle2DepthtanθC=DiameterofCircle2×DepthDiameterofCircle=2×Depth×tanθC

We have

nw=1.33Andna=1

From the figure, we can say that for air, the refractive angle is.

So according to Snell’s Law,

n1sinθ1=n2sinθ2nwsinθC=nasinθasinθC=nanwsinθasinθC=11.33×sin90°

sinθC=0.75θC=48.7°

We have

DiameterofCircle=2×DepthoftheSource×tanθCDiameterofCircle=2×0.8×tan(48.7)DiameterofCircle=1.82m

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Most popular questions from this chapter

Figure 33-32 shows four long horizontal layers A–D of different materials, with air above and below them. The index of refraction of each material is given. Rays of light are sent into the left end of each layer as shown. In which layer is there the possibility of totally trapping the light in that layer so that, after many reflections, all the light reaches the right end of the layer?

The leftmost block in Fig. 33-33 depicts total internal reflection for light inside a material with an index of refractionn1when air is outside the material. A light ray reaching point A from anywhere within the shaded region at the left (such as the ray shown) fully reflects at that point and ends up in the shaded region at the right. The other blocks show similar situations for two other materials. Rank the indexes of refraction of the three materials, greatest first.

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In the figure, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles ofθ1=θ2=θ3=50°with the direction of theyaxis. What percentage of the initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

Figure:

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