Question

A transparent cube contains a small air bubble. Its apparent distance is $$2\,cm$$  when seen through one face and $$5\,cm$$  when seen through other face. If the refractive index of the material of the cube is $$1.5,$$  the real length of the edge of cube must be

A. $$7\,cm$$
B. $$7.5\,cm$$
C. $$10.5\,cm$$  
D. $$\frac{{14}}{3}cm$$
Answer :   $$10.5\,cm$$
Solution :
As light travels from denser to rarer medium, so refractive index $$\left( \mu \right) = \frac{{{\text{real depth}}}}{{{\text{apparent depth}}}}$$
Refractive index $$\left( \mu \right) = 1.5$$
Net apparent depth $$ = 2 + 5 = 7\,cm$$
And real depth $$ = {\text{apparent depth}} \times \mu $$
$$\therefore $$ Real depth $$ = 1.5 \times 7 = 10.5\,cm$$

Releted MCQ Question on
Optics and Wave >> Ray Optics

Releted Question 1

When a ray of light enters a glass slab from air,

A. Its wavelength decreases.
B. Its wavelength increases.
C. Its frequency decreases.
D. neither its wavelength nor its frequency changes.
Releted Question 2

A glass prism of refractive index 1.5 is immersed in water (refractive index $$\frac{4}{3}$$ ). A light beam incident normally on the face $$AB$$  is totally reflected to reach on the face $$BC$$  if
Ray Optics mcq question image

A. $$\sin \theta \geqslant \frac{8}{9}$$
B. $$\frac{2}{3} < \sin \theta < \frac{8}{9}$$
C. $$\sin \theta \leqslant \frac{2}{3}$$
D. None of these
Releted Question 3

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
Ray Optics mcq question image

A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$
Releted Question 4

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
Ray Optics mcq question image

A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$

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