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Physics Ray Optics and Optical Instruments

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Physics Ray Optics and Optical Instruments Class 12th

A glass tumbler having inner depth of 17.5cm is kept on a table. A student starts pouring water $(μ = 4 / 3)$ into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

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Vishal Baghel

Contributor-Level 10

As observer is at O So height of water observed by observer

$\Rightarrow \frac{H}{μ_{ω}} = \frac{H}{(4 / 3)} = \frac{3 H}{4}$

given diagram (17.5 H) is height of observer

$S o \frac{3 H}{4} = 17.5 - H$

$\frac{7 H}{4} = 17.5$

7H = 70

H = 10

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Physics Ray Optics and Optical Instruments Class 12th

A point object moves towards a concave mirror with a speed $10 c m s^{- 1}$ along the principal axis. The magnitude of the velocity of object with respect to image when the object is at distance of 15cm from the pole is __ $c m s^{- 1}$ . (Focal length of the mirror kept at rest is 10cm )

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Raj Pandey

Contributor-Level 9

$v = \frac{f u}{u - f} = \frac{(- 10) (- 15)}{- 15 + 10} c m = - 30 c m$

$v_{image} = \frac{d v}{d t} = - {(\frac{v}{u})}^{2} \frac{d u}{d t} = - {(\frac{- 30}{- 15})}^{2} (10) c m s^{- 1} = - 40 c m s^{- 1}$

$V_{object} = \frac{d u}{d t} = + 10 c m s^{- 1}$

Relative velocity $= v_{object} - v_{image}$

$= 10 - (- 40) = 50 c m s^{- 1}$

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Physics Ray Optics and Optical Instruments Class 12th

A double convex lens is made of glass which has its refractive index of 1.55 for violet rays and 1.50 for red rays. If the focal length for violet rays is 20cm, then the focal length for red rays will be cm.

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Raj Pandey

Contributor-Level 9

$\frac{1}{20} = (1.55 - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f} = (1.50 - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

Divide (1) by (2), $\frac{f}{20} = \frac{0.55}{0.50}$

$f = 22 c m$

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Physics Ray Optics and Optical Instruments Class 12th

A fish moving up in water (μ = 4/3) with a speed of 4 cm/s observes a bird coming directly towards itself with a speed of 12 cm/s. Find the actual speed of the bird with respect to a stationary observer on the ground.

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Vishal Baghel

Contributor-Level 10

Velocity of bird = v
Velocity w.r.t. observer in water = (4/3)v; 12 = 4 + (3/4)v ⇒ v = 6 cm/s

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Physics Ray Optics and Optical Instruments Class 12th

The figure shows the initial position of a point source of light s, a detector D and lens L. Now at t = 0, all three starts moving towards right with different velocity as shown in figure. The times at which detector receives the maximum light, is (Assume that the detector is initially just touching the lens).

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alok kumar singh

Contributor-Level 10

$\frac{1}{0.9} = + \frac{1}{(10 ? 2 t)} + \frac{1}{2 t}$

t = 0.5 sec and t = 4.5 sec.

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Physics Ray Optics and Optical Instruments Class 12th

A ray of light is reflected by two perpendicular plane mirrors as shown. The angle θ is equal to:

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Vishal Baghel

Contributor-Level 10

At second surface,
i = 25°
r = 25°
∴ θ = I + r = 50°

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Physics Ray Optics and Optical Instruments Class 12th

The focal length f is related to the radius of curvature r of the spherical convex mirror by:

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alok kumar singh

Contributor-Level 10

Focus of a spherical convex mirror is in the same side of centre of curvature. Thus, f = + $\frac{1}{2} r .$

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Physics Ray Optics and Optical Instruments Class 12th

The difference of speed of light in the two media A and B $(υ_{A} - υ_{B})$ $_{}_{}$ is 2.6 * 107 m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum c = 3 * 108 ms-1)

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Raj Pandey

Contributor-Level 9

$μ_{B} = \frac{C}{v_{B}}$

$v_{B} = \frac{3 * 1 0^{8}}{1.47} = 20.408 * 1 0^{7}$

$v_{A} = 2.6 * 1 0^{7} + 20.408 * 1 0^{7} = 23 * 1 0^{7}$

$μ_{B} = \frac{C}{v_{B}} & μ_{A} = \frac{C}{v_{A}}$

= 1.127

$\approx 1.13$

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Physics Ray Optics and Optical Instruments Class 12th

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

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Raj Pandey

Contributor-Level 9

Velocity of light in medium 2

$= \frac{1}{\sqrt[]{μ_{m} \in_{m}}}$

$v_{2} = \frac{1}{\sqrt[]{μ_{0} μ_{r} \in_{0} \in_{r}}}$

$= \frac{1}{\sqrt[]{1 * μ_{0} \in_{0} * 4}}$

$v_{2} = \frac{1}{2 \sqrt[]{μ_{0} \in_{0}}}$

By snell's law for total internal Reflection

$μ_{2} s i n θ_{C} > μ_{1} s i n 90 °$

$θ_{c} > 30 °$

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Physics Ray Optics and Optical Instruments Class 12th

A ray of light is incident on a slab as shown in figure. The refractive index of medium of slab changes as μ = √(1 + y²). The angle made by ray with x – axis at y = √2 is

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Vishal Baghel

Contributor-Level 10

i = 60? , μ = √3
∴ 1 * sin (60? ) = √3 * sin r
=> r = 30?
∴ angle with x-axis = 60?

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