Ray Optics and Optical Test

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Ray Optics and Optical Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

At what angle will a ray of light be inclined on one face of an equilateral prism, so that the emergen ray may graze the second surface of the prism $$\left( {\mu = 2} \right)$$

A
$${30^0}\;$$

B
$$\,{90^0}$$

C
$$\;{45^0}$$

D
$$\;{60^0}$$

Solution

REF.Image
According to the question
For the emergent ray
$$\dfrac{sin r_{2}}{sin 90^{\circ}}= \dfrac{1}{\mu }$$
$$sin r_{2}=\dfrac{1}{2}$$
$$r_{2}= 30^{\circ}$$
Also, by the $$eq^{n}$$
$$r_{1}+r_{2}=A= 60^{\circ}$$
$$r_{1}+30^{\circ}= 60^{\circ}\Rightarrow r_{1}= 30^{\circ}$$
Then,
$$\dfrac{sin i}{sin r_{1}}=\mu \Rightarrow sin\, i= \dfrac{2}{2}=1$$
$$i = 90^{\circ}$$
Question 2
1 / -0

A thin equiconvex glass lens of refractive index $$1.5$$ has power of $$5D$$. When the lens is immersed in a liquid of refractive index $$\mu$$, it acts as a divergent lens of focal length $$100 \,cm$$. The value of $$\mu$$ of liquid is

A
$$4/3$$

B
$$3/4$$

C
$$15/11$$

D
$$8/3$$

Solution

Formula for focal length
$$\dfrac{1}{f}=\left(\dfrac{\mu_{2}}{\mu_{1}}=1\right)\left(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}\right)$$
Here, $$\dfrac{1}{f}=50\mu_{2}=1.5\mu_{1}=1$$
$$5=(1.5-1)\left[\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}\right]$$ ........ $$(1)$$
$$\therefore f=100\ cm=1\ m$$
$$\mu_{2}=1.5$$ let $$\mu_{1}=x$$
$$\therefore \dfrac{1}{1}=\left(\dfrac{1.5}{x}-1\right)\left(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}}\right)$$ ........ $$(2)$$
Dividing $$(1)$$ by $$(2)$$
$$\dfrac{5}{1}=\dfrac{0.5}{\dfrac{1.5}{x}-1}$$
$$\therefore \dfrac{1.5}{x}-1=\dfrac{0.5}{5}$$
$$\therefore \dfrac{1.5}{x}=\dfrac{11}{10}$$
$$\therefore \boxed{x=\dfrac{15}{11}}\therefore \mu_{1}=\dfrac{15}{11}=1.37$$
Question 3
1 / -0

A transparent cube contains a small air bubble. Its apparent 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
$$\dfrac{14}{3}\ cm$$

Solution

When viwed through (1),

$$\dfrac{n_2}{v}-\dfrac{n_1}{u}=\dfrac{n_2-n_1}{R}$$
$$\dfrac{1}{2}-\dfrac{1.5}{u}=\dfrac{0.5}{\infty}$$ ($$R=\infty$$ ,plane)
$$\dfrac{1}{2}=\dfrac{1.5}{u}$$
$$u=3cm$$

When viewed through (1),

$$\dfrac{n_2}{v}-\dfrac{n_1}{u}=\dfrac{n_2-n_1}{R}$$
$$\dfrac{1}{5}=\dfrac{1.5}{L-u}$$
$$L-u=7.5$$
$$L=7.5+3=10.5cm$$
Question 4
1 / -0

Two plano concave lenses of glass of refractive index 1.5 have radii of curvature 20 cm and 30 cm respectively. They are placed in contact with the curved surface towards each other and the space between them is filled with a liquid of refractive index 5/2. The focal length of the combination is (in cm)

A
6

B
-92

C
108

D
12

Solution
Question 5
1 / -0

A ball of negligible dimensions is drowned till an apparent measured depth of 15 m in a lake. What is the depth of the lake?

A
30

B
20

C
50

D
60

Solution

The real depth (d) of the lake is related to is apparent depth by :
$$\dfrac{d}{d'}=\mu \left[\mu : \text{Refractive index for water}=\dfrac{4}{3}\right]$$
$$\Rightarrow d=d'\mu \Rightarrow d=15\times \dfrac{4}{3}=20m.$$
$$\therefore $$ Real depth of lake $$=20 m$$.
Question 6
1 / -0

A double convex lens $$( \mu = 1.5 )$$ in air has its focal length equal to $$20\ cm$$. When immersed in water $$( \mu = 4 / 3 )$$ its focal length will be

A
$$20\ cm$$

B
$$80 / 9\ cm$$

C
$$360 / 9\ cm$$

D
$$80\ cm$$

Solution

Given,

Refractive indexes for, glass $${{\mu }_{g}}=1.5$$, water $${{\mu }_{w}}=\dfrac{4}{3}$$ and $${{\mu }_{a}}=1$$ .

If f is the focal length of the lens in air then

$$\dfrac{1}{{{f}_{a}}}=\left( \dfrac{{{\mu }_{g}}}{{{\mu }_{a}}}-1 \right)\times \left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)\,\,.........\,\,(1)$$

If f is the focal length of the lens in water then
$$\dfrac{1}{{{f}_{w}}}=\left( \dfrac{{{\mu }_{g}}}{{{\mu }_{w}}}-1 \right)\times \left( \dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}} \right)\,\,.........\,\,(2)$$

Divide equation (1) by (2)

$$\dfrac{\dfrac{1}{{{f}_{a}}}}{\dfrac{1}{{{f}_{w}}}}=\dfrac{\left( \dfrac{{{\mu }_{g}}}{{{\mu }_{a}}}-1 \right)}{\left( \dfrac{{{\mu }_{g}}}{{{\mu }_{w}}}-1 \right)}$$

$$ {{f}_{w}}=\left( \dfrac{{{\mu }_{g}}-{{\mu }_{a}}}{{{\mu }_{a}}}\times \dfrac{{{\mu }_{w}}}{{{\mu }_{g}}-{{\mu }_{w}}} \right){{f}_{a}} $$

$$ {{f}_{w}}=\left( \dfrac{1.5-1}{1}\times \dfrac{4/3}{1.5-4/3} \right)\times 20=80\,cm $$

Hence, focal length in water, $${{f}_{w}}=80\,cm$$
Question 7
1 / -0

The angle of a prism is $$6^0$$ and its refractive index for green light is 1.5. If a green ray passes through it, the deviation will be :-

A
$$30^0$$

B
$$15^0$$

C
$$9^0$$

D
$$3^0$$

Solution

Given,

Angle of prism, $$A={6}^{o}$$

Refractive index, $$\mu =1.5$$

Deviation, $$\delta =(\mu -1)A$$

$$=(1.5-1){6}^{o}$$

$$\delta ={3}^{o}$$
Question 8
1 / -0

A diverging meniscus lens has a focal length of -20 cm. If the lens is held 10 cm from the object, the magnification is :

A
-0.667

B
+0.667

C
-2

D
+2

Solution

given

Focal length, $$f=-20cm$$

Object distance, $$u=10cm$$

From len's formula

$$\cfrac{1}{f}=\cfrac{1}{v}-\cfrac{1}{u}$$

$$\Rightarrow$$ $$\cfrac{1}{-20}=\cfrac{1}{v}+\cfrac{1}{10}$$

$$\Rightarrow$$ $$v=-\cfrac{20}{3}cm$$

Magnification, $$m=\cfrac{v}{u}$$

$$=\cfrac{-20}{3\times -10}$$

$$=\cfrac{2}{3}=0.667$$

$$m=0.667$$
Question 9
1 / -0

Given that, velocity of light in quartz $$ = 1.5 \times {10^8}m/s$$ and velocity of light in glycerin $$ = \left( {\dfrac{9}{4}} \right) \times {10^8}m/s$$ Now a slab made of quartz is placed in glycerin as shown . The shift of the object produced by slab is :

A
$$6 cm$$

B
$$3.55 cm$$

C
$$9 cm$$

D
$$2 cm$$

Solution

First find the value of the refractive index for the two mediums.

$$n$$(of quartz with respect to glycerine) $$=(9/4)*1/1.5=3/2$$

Now lateral shift $$= t(1-1/n)$$

$$= 0.18*(1-2/3)$$

$$= 0.06 m= 6 cm$$
Question 10
1 / -0

An angular magnification ( magnifying power ) of 30X is desired using an object 1.25 cm and an eyepiece of focal length 5 cm. If compound microscope is to be set up then the separation between the objective lens and the eyepiece.

A
11.67 cm

B
21.67 cm

C
31.67 cm

D
None of these

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Re-Attempt Weekly Quiz Competition

Ray Optics and Optical Test - 51

Result

Ray Optics and Optical Test - 51

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SHARING IS CARING

Question 1

$${30^0}\;$$

$$\,{90^0}$$

$$\;{45^0}$$

$$\;{60^0}$$

Solution

Question 2

$$4/3$$

$$3/4$$

$$15/11$$

$$8/3$$

Solution

Question 3

$$7\ cm$$

$$7.5\ cm$$

$$10.5\ cm$$

$$\dfrac{14}{3}\ cm$$

Solution

Question 4

6

-92

108

12

Solution

Question 5

30

20

50

60

Solution

Question 6

$$20\ cm$$

$$80 / 9\ cm$$

$$360 / 9\ cm$$

$$80\ cm$$

Solution

Question 7

$$30^0$$

$$15^0$$

$$9^0$$

$$3^0$$

Solution

Question 8

-0.667

+0.667

-2

+2

Solution

Question 9

$$6 cm$$

$$3.55 cm$$

$$9 cm$$

$$2 cm$$

Solution

Question 10

11.67 cm

21.67 cm

31.67 cm

None of these

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