In above figure, light is incident at angle $$\theta _{1}=40.1^{0}$$ on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If $$n_{1}=1.30$$, $$n_{2}=1.40$$, $$n_{3}=1.32$$ and $$n_{4}=1.45$$ what is the value of (a) $$\theta _{5}$$ in the air and (b) $$\theta _{4}$$ in the bottom material?
(a) Approximating $$n = 1$$ for air, we have
$$n_{1}\sin \theta _{1}=\left ( 1 \right )\sin \theta _{5}\Rightarrow 56.9^{0}=\theta _{5}$$.
and with the more accurate value for $$n_{air}$$ in Table below, we obtain $$56.8^{0}$$.
(b) Equation $$n_{1}\sin \theta _{c}=n_{2}\sin 90^{0}$$ leads to,
$$n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}=n_{3}\sin \theta _{3}=n_{4}\sin \theta _{4}$$.
so that. $$\theta _{4}=\sin ^{-1}\left ( \frac{n_{1}}{n_{4}}\sin \theta _{1} \right )=35.3^{0}$$.
A pole of length $$1.00 m$$ stands half dipped in a swimming pool with water level $$50.0 cm$$ higher than the bed. The refractive index of water is $$1.33$$ and sunlight is coming at an angle of $$45^o$$ with the vertical. Find the length of the shadow of the pole on the bed.
A light ray falling at an angle of $$45^o$$ with the surface of a clean slab of ice of thickness $$1.00 m$$ is refracted into it at an angle of $$30^o$$. Calculate the time taken by the light rays, to cross the slab. Speed of light in vacuum $$= 3 \times 10^8 m/s$$.
A vessel contains a slab of glass $$8\ cm$$ thick and of refractive index $$1.6$$. Over the slab, the vessel is filled by oil of refractive index $$\mu$$ upto height $$4.5\ cm$$ and also by another liquid i.e., water of refractive index $$\cfrac{4}{3}$$ and height $$6\ cm$$. As shown in figure. As observer looking down from above, he observes that, a mark at the bottom of the glass slab appears to be raised up to position $$6\ cm$$ from the bottom of the slab. Refractive index ($$\mu$$) of oil is:
At what value of the angle of incident $$ \theta_{1} $$ is a shaft of light reflected from the surface of water perpendicular to the refracted shaft?
A ray of white light traveling through fused quartz is incident at a quartz–air interface at angle $$\theta _{1}$$. Assume that the index of refraction of quartz is $$n=1.456$$$ at the red end of the visible range and $$n=1.470$$ at the blue end. If $$\theta _{1}$$ is (a) $$42.00^{0}$$, (b) $$43.10^{0}$$ and (c) $$44.00^{0}$$ is the refracted light white, white dominated by the red end of the visible range or white dominated by the blue end of the visible range or is there no refracted light?
In above figure, where $$n_{1}=1.70$$, $$n_{2}=1.50$$ and $$n_{3}=1.30$$, light refracts from material 1 into material 2. If it is incident at point $$A$$ at the critical angle for the interface between materials 2 and 3, what are (a) the angle of refraction at point $$B$$ and (b) the initial angle $$\theta$$? If, instead, light is incident at $$B$$ at the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at point $$A$$ and (d) the initial angle $$\theta$$? If, instead of all that, light is incident at point $$A$$ at Brewster’s angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point $$B$$ and (f) the initial angle $$\theta$$?
A light ray from air is incident (as shown in figure) at one end of a glass fibre (refractive index, $$\mu=1.5$$) making an incidence angle of 60 on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to reverse the straight fiber of length 1 km?
When light travels from glass to air, the incident angle is $$\theta_1$$ and the refractive angle is $$\theta_2$$. The true relation is
The graph between sine of angle of refraction $$(sin\ r)$$ in medium $$2$$ and sine of angle of incident $$(sin\ i)$$ in medium $$1$$ indicates that $$(tan 360^o\approx \dfrac{3}{4})$$
Write true or false for each statement A ray of light when passes from glass to air , bends towards the normal.