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Geometrical Optics (Refraction)

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Q.

Two lenses shown are illuminated by a beam of parallel light from the left. Lens B is then moved slowly toward lens A. The beam emerging from lensB is

                                                     

Q.

In the arrangement shown below, the image of the extended object as seen by the observer is

                                       

Q.

The refracting angle of a prism is A and refractive index of the material of prism is cot(A/2). The angle of minimum deviation will be

Q.

A small straight rod is placed at an inclination with the optical axis of a thin lens as shown in the figure. The base of the rod is on the optical axis and at a distance 2f (f = focal length of the lens) from the lens. The image of the rod would be

                                                                 

Q. If plane side of a plano convex lens is silvered what is the effective focal lenght . If curved side is sivered then what is effective focal lenght Please tell me the formula and answer in both these cases?

A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm.

Q. A fixed cylindrical tank of height H=4m and radius R=3m is filled up with a liquid. An observer through a telescope fitted at the top of the wall of the tank and inclined at angle theta= 45 degree with the vertical. When the tank is completely filled with liquid, he notices an insect , which is the center of the bottom of the tank. At t=0 , he opens a cork of radius r=3cm at the bottom of tank. The insect moves in such a way that it is visible for a certain time. Determine (a) the refractive index of the liquid (b) the velocity of insect as a function of time. How did the value of x is determined?

Applying the Bernoulli's equation for the given setup: P 0​+ 2 1​×2×ρv 2 =P 0​+2ρg+ 2 h​+ρgh So, velocity of efflux comes out to be v= 2gh​Now, for the distance covered in vertical direction: 2 1​gt 2 = 2 h​So, t= g h​​So, the ranfe of the efflux will be: R=v×t R= 2​h

Q. What will be formula for calculations of apparent depth when refractive index of material and real depth is given in question and what will be conditions for it?

Refractive Index = real depth/apparent depth

When a ray of light moves from one medium to another there is a change in velocity and direction of ray due to refraction which results in false appearance of depth of the material. The actual depth that a transparent medium has is known as real depth. Note − Real depth is always greater than apparent depth.

Q. A telescope has objective lens of focal length 15m and eyepiece of focal length 1cm. If it is used to view the moon , what is the diameter of the image of moon formed by objective lens? Diameter of moon is 3.48 ×10^6 and radius of lunar orbit is 3.8 ×10^8?

a) | em / m | = | f₀ / fe |

f₀ = Focal length of objective

fe = Focal length of eyepiece

| m | = 15 × 100 / 1 = 1500

∵ image formed is inverted

∵ Angular magnification = + 1500


(b) Angle subtended by moon at object = angle of image at objective

D/R = d/f₀

3.4 × 10⁶ / 3.8 × 10⁸ = d/15

d = 3.4/3.8 × 10⁻² × 15 m

d = 13.4 cm