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As shown in Fig. $36-7$, a light ray $I O$ is incident on a small plane mirror. The mirror reflects this ray back onto a straight ruler $S C$ which is $1 \mathrm{~m...

Question

As shown in Fig. $36-7$, a light ray $I O$ is incident on a small plane mirror. The mirror reflects this ray back onto a straight ruler $S C$ which is $1 \mathrm{~m}$ away from and parallel to the undeflected mirror MM. When the mirror turns through an angle of $8.0^{\circ}$ and assumes the position $M^{\prime} M^{\prime}$, across what distance on the scale will the spot of light move? (This device, called an optical lever, is useful in measuring small deflections.) When the mirror turns throug

As shown in Fig. $36-7$, a light ray $I O$ is incident on a small plane mirror. The mirror reflects this ray back onto a straight ruler $S C$ which is $1 \mathrm{~m}$ away from and parallel to the undeflected mirror MM. When the mirror turns through an angle of $8.0^{\circ}$ and assumes the position $M^{\prime} M^{\prime}$, across what distance on the scale will the spot of light move? (This device, called an optical lever, is useful in measuring small deflections.) When the mirror turns through $8.0^{\circ}$ the normal to it also turns through $8.0^{\circ}$, and the incident ray makes an angle of $8.0^{\circ}$ with the normal $N O$ to the deflected mirror $M^{\prime} M^{\prime}$. Because the incident ray $I O$ and the reflected ray $O R$ make equal angles with the normal, angle $I O R$ is twice the angle through which the mirror has turned, or $16^{\circ}$. Then $$ \overline{I R}=\overline{I O} \tan 16^{\circ}=(1.0 \mathrm{~m})(0.287)=29 \mathrm{~cm} $$



Answers

Total Internal Reflection
In Fig. 33-62, a light ray in air is incident at angle $\theta_{1}$ on a block of transparent plastic with an index of refraction of $1.56 .$ The dimensions indicated are $H=2.00 \mathrm{cm}$ and $W=3.00 \mathrm{cm} .$ The light passes through the block to one of its sides and there undergoes reflection (inside the block $)$ and possibly refraction (out into the air). This is the point of first reflection. The reflected light then passes through the block to another of its sides $-$ a point of second reflection. If $\theta_{1}=40^{\circ},$ on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of (c) first reflection and (d) second reflection, give the angle of refraction; if not, answer "none." If $\theta_{1}=70^{\circ},$ on which side is the point of (e) first reflection and (f) second reflection? If there is refraction at the point of (g) first reflection and (h) second reflection, give the angle of refraction; if not, answer "none."


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