ray optics and optical instruments

Two convex lenses of same focal lengths but of aperture A₁ and A₂ (A₂ < A₁)_, are used as the objective lenses in two astronomical telescopes having identical eye-pieces. The ratio of their resolving powers is

• $\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}$

• 1 : 1

• $\frac{{\mathrm{A}}_2}{{\mathrm{A}}_1}$

• data insufficient

A beam of light converges at a point P. A concave lens of focal length 16 cm is placed in the path of this beam 12 cm from P. The location of the point, from the lens, at which the beam would now converge is

• 48 cm

• 45 cm

• 80 cm

• 90 cm

A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principle axis. If the power of original lens is 4D, then the power of a cut lens will be

• 2D

• 3D

• 4D

• 8D

When a light enters a refracting medium, it is found that the magnitude of the angle of refraction is equal to half the angle of reflection. If µ is the refractive index of the medium, then the angle of incidence is

• $2 {\sin }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

• $2 {\cos }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

• ${\cos }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

• ${\sin }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

A compound microscope has a magnifying power of 100, when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. The
focal length of eye-piece is

• 4 cm

• 2 cm

• 6 cm

• 5.2 cm

When a ray of light enters a glass lens surrounded by air, it slows down. As it  leaves the glass, does its speed increases, decreases or stay the same ? Choose the correct answer from the following.

1. Its speed decreases as the ray is propagating in a medium with higher refractive index.
2. Its speed increases as the refractive index of air is less than that of glass.
3. The speed will stay the same because the speed of light is a universal constant.

• Only I

• Only II

• Only III

• None of these

A telescope consists of two thin lenses of focal lengths 0.3 m and 3 cm respectively. It is focused on moon which subtends an angle of 0.5° at the objective. Then, the angle subtended at the eye by the final image will be

• 5°

• 0.25°

• 0.5°

• 0.35°

An object is placed at a distance of 10 cm from a co-axial combination of two lenses A and B in contact. The combination forms a real image three times the  size of the object. If lens B is concave with focal length of 30 cm, the nature and focal length of lens A is

• convex, 12 cm

• concave, 12 cm

• convex, 6 cm

• convex, 18 cm

The radius of curvature of a concave mirror, measured by a spherometer is given by $\mathrm{R} = \frac{{\mathrm{l}}^2}{6\mathrm{h}} + \frac{\mathrm{h}}{2}$. The value of l and h are 4.0 cm and 0.065 cm respectively, where l is measured by a meter scale and h by a spherometer. The relative error in the measurement of R is

• 0.06

• 0.6

• 0.023

• 2.3

Two thin lenses when placed in contact, then the power of combination is +10D. If they are kept 0.25 m apart, then the power reduces to +6D. The focal lengths of the lenses (in m) will be

• 0.5 and 0.125

• 0.5 and 0.75

• 0.125 and 0.75

• Both have same focal length i.e. 1.25