Ray Optics and Optical Test

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Ray Optics and Optical Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

Why are red coloured lights are used in traffic signals to stop the vehicles?

A
minimum wavelength and less scatter.

B
maximum wavelength and more scatter.

C
maximum wavelength and less scatter.

D
less wavelength and less scatter.

Solution

We know among the seven colours of white light, red colour has maximum wavelength. That is why red colour is least scattered by atmospheric dust and other particles. Hence red colour is used to indicated any danger sign.
Question 2
1 / -0

The colour which has least critical angle is

A
Orange

B
Red

C
Violet

D
Green

Solution

$$\begin{array}{l}\text { For total internal reflection to take place. } \\\qquad \begin{array}{l}\mu\sin\theta_{c}=1 \\\theta_{c}=\sin ^{-1}\left(\frac{1}{\mu}\right)\end{array}\end{array}$$
$$\begin{array}{l}\text { As a fact, the refractive index for a ray is inversely } \\\text { proportional to its wavelength. }\end{array}$$
$$\begin{array}{l}\quad \mu \times \frac{1}{\lambda} \\\text { Since violet has shortest wavelength it's critical } \\\text { angle is also low }\end{array}$$
Question 3
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A bird is flying $$12 m$$ above the surface of a pond. What is the apparent position of the bird as viewed by a fish $$1m$$ below the surface? ($$_{a}\mu _{w}=\cfrac{4}{3}$$)

A
$$16 m$$

B
$$17 m$$

C
$$15 m$$

D
$$13 m$$

Solution

$$h=12 \ m , h'=?$$

$$_a\mu_w=\dfrac{4}{3} , d=1m$$

$$_a\mu_w=\dfrac{h'}{h_1} : \dfrac{4}{3}=\dfrac{h}{12}$$

$$ h'=\dfrac{4}{3}\times12=16m$$

Total height $$=h'+d=(16+1)m=17m$$
Question 4
1 / -0

The bending of light as it passes from one medium into another is commonly known as

A
Reflection

B
Refraction

C
Scattering

D
Dispersion

Solution

In refraction ray of light passes from one medium to another medium. The ray of light bends towards normal in the denser medium.
Question 5
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ABCD represents a glass slab and PQRS indicates the path of a light ray passing through the slab.If the refractive index of the glass is $$\sqrt{3}$$, find 'x'.

A
$$5\sqrt{2}$$

B
$$4\sqrt{3}$$

C
$$2\sqrt{3}$$

D
$$5\sqrt{3}$$

Solution

Given r = 30 degree. Since r.i = $$ \sqrt 3$$. using $$ \mu = sin i / sin r $$, we get i = 60 degree.
Now lateral shift = thickness $$\times$$ sin (i - r) / cos r = 15 $$\times$$ (1/2) (2 / $$ \sqrt 3) = 5 \sqrt 3 $$
Question 6
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A bird flying above a pond starts moving vertically down towards the water below at a speed of $$v \ m s^{-1}$$. Find its apparent velocity as viewed by a fish located at a depth of $$d$$ m below the surface of water of refractive index $$\mu $$.

A
$$\mu v$$

B
$$\cfrac{\mu}{ v}$$

C
$$\mu^2 v$$

D
$$\mu v^2$$

Solution

As the refractive index, $$\mu=$$apparent distance/true distance=apparent velocity/true velocity.
So, apparent velocity is $$\mu\times$$ true velocity=$$\mu\times v=\mu v$$
Question 7
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When light travels from one medium into another it suffers

A
Reflection

B
Refraction

C
Dispersion

D
None of these

Solution

When light travels from one medium into another it suffers refraction,
Question 8
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The figure shows cross section of a hollow glass tube of internal radius $$r$$, external radius $$R$$ and index of refraction $$n$$. For two rays DE and ABC (in which DE lies on ODE and DE is parallel to BC), the separation $$r_1$$ will be :

A
$$r_1 = (n - 1) R$$

B
$$r_1 = n^2 R$$

C
$$r_1 = nr$$

D
$$r_1 = n^2 r$$

Solution

In given figure $$\theta$$ is angle of refraction and $$\alpha$$ is angle of incidence for ray ABC.

Required length = $$r_1=BP$$

Since $$DE\parallel BC\implies \angle BOP=\theta$$

Now, in $$\Delta BOP:-$$

$$r_1=BP=OB\sin\theta=R\sin \theta$$

$$\implies \sin\theta=\dfrac{r_1}{R}$$

In $$\Delta OAB:-$$

$$\angle A=90^{o}$$
$$\sin \alpha=\dfrac{r}{R}$$

Now, at refraction of ray $$ABC$$

$$\dfrac{\sin\theta}{\sin\alpha}=n$$

$$\implies \dfrac{r_1/R}{r/R}=n\implies \dfrac{r_1}{r}=n$$

$$\implies r_1=nr$$

Answer-(C)
Question 9
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A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will

A
separate part of the red color from the green and blue colors.

B
separate part of the blue color from the red and green colors.

C
Separate all the three colors from the other two colors.

D
not separate even partially any color from the other two colors.

Solution

At point A, for total internal reflection to take place, $$\mu \ sin \ i > 1$$
Hence $$\mu>\sqrt{2}$$ for total internal reflection to take place,
Thus green and blue colours suffer total internal reflection whereas red just refracts and gets separated from the other two.
Question 10
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A thin lens with focal length f to be used as magnifying glass. Which of the following statements regarding the situation is true?

A
A converging lens may be used, and the object be placed at a distance greater than 2f from the lens.

B
A diverging lens may be used, and the object be placed between f and 2f from the lens.

C
A converging lens may be used, and the object be placed at a distance less than f from the lens.

D
A diverging lens may be used, and the object be placed at any point other than the focal point.

Solution

A converging lens, magnifies the image of an object if it is placed at a distance less than the focal length of the lens.