Ray Optics and Optical Test

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Ray Optics and Optical Test - 69

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Weekly Quiz Competition

Question 1
1 / -0

A beam of light is converging towards a point on the screen. If a plane parallel plate of glass of refraactive in $$\mu $$ and thickness t is introduced in the path of the beam, the convergent point is shifted

A
$$t[1-\frac{1}{\mu }] $$ away

B
$$t[1+\frac{1}{\mu }] $$ nearer

C
$$t[1+\frac{1}{\mu }] $$ away

D
$$t[1-\frac{1}{\mu }] $$ nearer

Solution

When glass plate of thickness t is introduced, the optical path increases by (t/μ).
So the convergence point shifts by t – (t/ μ)

i.e. t[1 – (1/ μ)] nearer.
Question 2
1 / -0

Two identical thin isosceles prism of refracting angle 'A' and refractive index $$ \mu $$ are placed their bases touching each other. Two parallel rays of light are incident on this system as shown The distance of the point where the rays converge from the prism is:

A
$$ \dfrac { h }{ \mu A } $$

B
$$ \dfrac { h }{ A } $$

C
$$ \dfrac { h }{ \left( \mu -1 \right) a } $$

D
$$ \dfrac { \mu h }{ \left( \mu -1 \right) a } $$

Solution

$$ \begin{array}{l} \text { since } \tan \delta=\frac{h}{f} \Rightarrow f=\frac{h}{\tan \delta} \\ \text { further, } \delta=(\mu-1) A \Rightarrow f=\frac{h}{(\mu-1) A} \\ \therefore f=\frac{h}{(\mu-1) A} \end{array} $$
Question 3
1 / -0

A ray of light makes normal incidence on the diagonal face of a right angled prism as shown in figure. If $$ \theta = 37^o $$, then the angle of deviation after second step (from AB) is (sin $$ 37^o = 3/5 $$ )

A
$$ 53^o $$

B
$$ 74^o $$

C
$$ 106^o $$

D
$$ 90^o $$

Solution

When light strike face $$A B$$ $$\Rightarrow \sin _{i c}=\frac{1}{\mu}\left(\therefore i_{c}=\right.$$ critical angle $$)$$
$$\Rightarrow \sin _{i c}=\frac{3}{5}$$
$$\Rightarrow \quad i_{c}=37^{\circ}$$
But in face incidance angle $$=53^{\circ}$$
$$\therefore$$ reflection takes place
$$\angle i\rangle<\angle i_{c}$$
9n face BC Incidence angle $=37^{\circ}$
$$\begin{array}{l}\quad i=i c\\\therefore\quad\angle\gamma=90\end{array}$$
$$c D$$ is divergent ray angle blw incident and divergent ray is $$53^{\circ}$$ (from figure)
Hence (A) is correct
Question 4
1 / -0

For water $$\mu = \dfrac{4}{3}$$ and the velocity of light in vacuum is $$3 \times 10^8 m/s$$, the time taken for light to travel a distance of $$450\ m$$ in water will be.

A
$$2 \mu s$$

B
$$1.5 \mu s$$

C
$$1 \mu s$$

D
$$3 \mu s$$

Solution
Question 5
1 / -0

A convex lens of focal length $$\frac{1}{3}m$$ forms a real inverted image twice in size of the object. The distance of the object from the lens is

A
$$0.5\,m$$

B
$$0.166\,m$$

C
$$0.33\,m$$

D
$$1\,m$$

Solution
Question 6
1 / -0

A shallow glass dish is $$4.00\ cm$$ wide at the bottom, as shown in figure. When an observer's eye is positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is filled with water, the observer sees the centre of the bottom of the dish. Find the height of the dish. $$(\mu_{w} = 4/3)$$.

A
$$1.4\ cm$$

B
$$2.4\ cm$$

C
$$3.4\ cm$$

D
$$3.1\ cm$$

Solution

Option B is correct
Question 7
1 / -0

A diverging meniscus of radii of curvatures $$25\ cm \ and \ 50 \ cm $$ has a refractive index $$1.5$$. Its focal length is :

A
$$-50cm$$

B
$$-100cm$$

C
$$100cm$$

D
$$50cm$$

Solution
Question 8
1 / -0

Consider a hemisphere of radius R with centre of curvature at origin O, as shown. Refractive index of material of the hemisphere varies as $$\mu = \frac{2R}{2R-x}$$. Where x is x-coordinate of material point. A ray travelling in air in xy-plane is grazingly incident at O, as shown in the figure. Now answer the following question.
Deviation suffered by the ray just before it comes out of the hemispherical surface

A
lies between $$ 0^o and 30^o$$

B
lies between $$ 30^o and 45^o$$

C
is greater than $$60^o$$

D
is equal to $$60^o$$
Question 9
1 / -0

A liquid of refractive index $$1.5$$ is poured into a cylindrical jar of radius $$20$$ cm up to a height of $$20$$ cm. A small bulb is lighted at the centre of the bottom of the jar. Find the area of the liquid surface through which the light of the bulb passes into air.

A
$$1005$$ $$m^2$$

B
$$0.01005$$ $$m^2$$

C
$$10.05$$ $$m^2$$

D
$$0.1005$$ $$m^2$$

Solution

Correct Answer: Option D
Step 1: Find the critical angle
Refer figure $$1$$
Applying Snell's law
$$\mu_{w} sin c = \mu_{a} sin 90^0$$

$$\mu_{w}= \dfrac{1}{\sin c}$$

$$\sin c = \dfrac{1}{\mu_{w}}$$ .......$$(I)$$

Step 2: Find the area of circle of vision
From figure
$$A = \pi r^2$$
$$r = h\ tanc$$
From $$(I)$$

$$\tan c = \dfrac{1}{\sqrt{\mu_{w}^2-1}}$$ ........$$(II)$$

$$r = \dfrac{h}{\sqrt{\mu_{w}^2-1}}$$

So,
Area of circle $$= \pi r^2 = \dfrac{\pi \times h^2}{\mu_{w}^2-1} = \dfrac{\pi \times (0.2)^2}{1.5^2 - 1}$$

$$= 0.1005m^2$$

Hence, the correct answer is option D.
Question 10
1 / -0

A beam of light considering of red, green and blue colours is incident on an isosceles right angled prism as shown in the figure. the refractive indices of the material of the prism for red, green and blue colours are 1.39, 1.43 and 1.47 respectively. the prism will

A
separate red colours from green and blue colours

B
separate blue colours from red and green colours

C
separate green colour from, red and blue colours.

D
separate all the three colours from one another.

Solution