Subjective Type

A large square container with thin transparent vertical walls and filled with water (refractive index $$\dfrac{4}{3}$$) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is _______.

Solution

Assume that observer see the image of object through edge $$\Rightarrow a = 45^{\circ}$$

$$AB = \dfrac{12 d \alpha}{\cos \alpha} = \dfrac{x d\theta }{\cos \theta}$$

Applying snell's law

$$\dfrac{4}{3} \sin a = 1. sin a $$

$$\dfrac{4}{3} \cos a \ da = \cos \theta \ d \theta $$

$$\Rightarrow \dfrac{9}{\cos^2 \alpha} = \dfrac{x}{\cos^2 \theta }$$

$$1. \sin \theta = \dfrac{4}{3} \sin \alpha$$

$$\Rightarrow \sin \theta = \dfrac{2 \sqrt{2}}{3}$$

$$\Rightarrow x = 18 \times \dfrac{1}{9} = 2$$

$$d = 2 \times \sin (\theta - \alpha)$$

$$= 4 \times \dfrac{1}{\sqrt{2}} \left(\dfrac{2 \sqrt{2}}{3} - \dfrac{1}{3}\right) = \dfrac{8-2\sqrt{2}}{3}$$

$$= 1.73 \approx 2$$

SIMILAR QUESTIONS

Optics

A small piece of wood is floating on the surface of a $$2.5 m$$ deep lake. Where does the shadow form on the bottom when the sun is just setting? refractive index of water $$=4/3$$.

Optics

A glass sphere has radius $$R=5.0$$ cm and index of refraction $$1.6$$. A paperweight is constructed by slicing through the sphere along a plane that is $$2.0$$ cm from the center of the sphere, leaving height $$h = 3.0$$ cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance $$d = 8.0$$ cm from the tabletop. When viewed through the paperweight, how far away does the tabletop appear to be to the observer?

Optics

(a) Prove that a ray of light incident on the surface of a sheet of plate glass of thickness $$t$$ emerges from the opposite face parallel to its initial direction but displaced sideways,as in above figure. (b) Show that, for small angles of incidence $$\theta$$, this displacement is given by $$x=t\theta \frac{n-1}{n}$$. where $$n$$ is the index of refraction of the glass and $$\theta$$ is measured in radians.

Optics

An under water swimmer is at a depth of 12 m below the surface of water. A bird is at a height of 18 m from the surface of water, directly above his eyes. For the swimmer the bird appears to be at a distance from the surface of water equal to : (Refractive index of water is 4/3)

Optics

A layer of oil of refractive index $$ n_o $$ floats on water of refractive index $$ n_w $$. A beam of light is directed upward from a source in the water. Show that the critical angle for a total internal reflection is independent of $$ n_o $$, even though, for angles close to C (critical angle), the total internal reflection always takes place at the oil-air surface.

Optics

Light incident on a surface separating two media is partly reflected and partly refracted as shown in figure $$ \mu_1 $$ and $$ \mu_2 $$ are the respective indices of the two media and $$ C $$ is the critical angle for the interface. Which of the equation is correct ?

Optics

A ray of light travels from a medium of refractive index $$ \mu $$ to air . Its angle of incidence in the medium is $$ \theta $$ , measured from the normal to the boundary and its angle of deviation is $$ \delta $$ with the angle of refraction $$ \phi $$. A graph is plotted between $$ \delta $$ and $$ \theta $$ which is shown in the figure. Choose the correct relation from the following

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