The focal lengths of the objective and of the eye-piece of a compound microscope are f₀ and f_e respectively. If L is the tube length and D, the least distance of distinct vision, then its angular magnification, when the image is formed at infinity is

• $\left(1 - \frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}}\right) \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\left(1 + \frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}}\right) \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}} \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}} \left(1 + \frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eye-piece is 36 cm and the final image is formed at infinity. The focal length f_o of the objective and f_e of the eye-piece are respectively

• 45 cm and 9 cm

• 50 cm and 10 cm

• 7.2 cm and 5 cm

• 30 cm and 6 cm

If the reflected image formed is magnified and virtual, then the mirror system is

• concave only

• convex only

• plane

• concave or convex

A vessel of depth x is half filled with oil of refractive index µ₁ and the other half is filled with water of refractive index µ₂. The apparent depth of the vessel when viewed from above is

• $\frac{\mathrm{x} \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}{2 {\mathrm{\mu }}_1{\mathrm{\mu }}_2}$

• $\frac{\mathrm{x} {\mathrm{\mu }}_1{\mathrm{\mu }}_2}{2 \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{x} {\mathrm{\mu }}_1{\mathrm{\mu }}_2}{\left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{2\mathrm{x} \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}{{\mathrm{\mu }}_1{\mathrm{\mu }}_2}$

The refractive index and the permeability of a medium are respectively 1.5 and 5 x 10^-7 Hm^-1. The relative permittivity of the medium is nearly

• 25

• 15

• 6

• 10

A square wire of side 1 cm is placed perpendicular to the principal axis of a concave mirror of focal length 15 cm at a distance of 20 cm. The area enclosed by the image of the wire is

• 4 cm²

• 6 cm²

• 9 cm²

• 8 cm²

A thin prism P of refracting angle 3° and refractive index 1.5 is combined with another thin prism Q of refractive index 1.6 to produce dispersion without deviation. Then the angle of prism Q is

• 3°

• 4°

• 3.5°

• 2.5°

Two piano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index $\frac{4}{3}$. Then the combination is 

• convex of focal length 70 cm

• concave of focal length 70 cm

• concave of focal length 66.6 cm

• convex of focal length 66.6 cm

If the ratio of amounts of scattering of two light waves is 1 :4, the ratio of their wavelengths is

• 1 : 2

• $\sqrt{2} : 1$

• $1 : \sqrt{2}$

• 1 : 1

If the angle of minimum deviation is of 60° for an equilateral prism, then the refractive index of the material of the prism is

• 1.41 

• 1.5

• 1.73

• 1.33