Ray Optics and Optical Test

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Ray Optics and Optical Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

Assertion: Two convex lenses joined together cannot produce an achromatic combination.
Reason : The condition for achromatism is $$\dfrac{\omega _1}{f_1}+\dfrac{\omega _2}{f_2}=0$$ where symbols have their usual meaning.

A
If both Assertion 'and Reason are correct and Reason is the correct explanation of Assertion

B
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

C
If Assertion is correct but Reason is incorrect

D
If Assertion is incorrect but Reason is correct

Solution

$$ \begin{array}{l} \text { Lens which is made by a combination of two } \\ \text { different types of lenses carrying different } \\ \text { focal powers in a manner such that the image } \\ \text { formed by the light of both the combined } \\ \text { lenses are free from chromatic aberration } \\ \text { or achromatism is called achromatic combination. } \\ \text { two convex lenses can produce achromatic. } \\ \text { combination when distance between then } \\ \qquad d=\dfrac{f_{1}+f_{2}}{2} \text { where } f_{1}, f_{2} \text { are focal length } \end{array} $$
$$ \begin{array}{l} \text { But in given Combination } d=0 \\ \text { So Assertion is Correct } \\ \text { The condition for achromatism is } \\ \dfrac{\omega_{1}}{f_{1}}+\dfrac{\omega_{2}}{f_{2}}=0 \text{ where symbols have their}\\ \text { usual meaning. } \\ \text { Hence option 'A' is correct. } \end{array} $$
Question 2
1 / -0

When light moving in one medium falls at the surface of another medium, _______ light returns back to the same medium.

A
all of

B
a part of

C
no

D
either all or no

Solution

Light moving in one medium when falls at the surface of another medium, part of light returns to the same medium. Some part is transmitted and the rest is absorbed. No material is a perfect reflector. Almost all surfaces absorb some part of light.
Question 3
1 / -0

In an electron microscope the accelerating voltage is increased from 20 kV to 80 kV, the resolving power ofthe microscope will become.

A
2R

B
$$\frac {2}{R}$$

C
4R

D
3R

Solution

We know that wavelength and accelerating voltage for an electron is related to each other as follows
$$\lambda \propto \frac{1}{\sqrt V}$$ [V is'potential applied]
and resolving power $$\propto \frac{1}{\lambda}$$.
So, resolving power $$\propto \sqrt {V}$$
Now,if potential used is increased 4 times, resolving power will be increased 2 times.
So, if resolving power earlier is R. It becomes 2R.
Question 4
1 / -0

Assertion: A double convex lens ($$\mu$$ = 1.5) has focal length 10 em, When the lens is immersed in water ($$\mu$$ = 4/3) its focal length becomes 40 cm.
Reason: $$\frac{1}{f}=\frac{\mu_1-\mu_m}{\mu_m}=\left ( \frac{1}{R_1}-\frac{1}{R_2} \right )$$.

A
Both assertion and reason are true but the reason is the correct explanation of assertion

B
Both assertion and reason are true but the reason is not the correct explanation of assertion

C
Assertion is true but reason is false

D
Both the assertion and reason are false

E
Reason is true but assertion is false

Solution

Given: a double convex lens($$\mu=1.5$$) has focal length 10 cm, the lens is immersed in water $$\left(\mu = \dfrac43\right)$$
Solution:
If focal length of the lens when immersed in water be $$f_w$$
Focal length in air can be calculated by the formula,
$$\dfrac 1{f_a}=\left(\dfrac {\mu_1}{\mu_2}-1\right)\left(\dfrac 1{R_1}-\dfrac 1{R_2} \right)\\\implies \dfrac 1{f_a}=\left(\dfrac {1.5}{1}-1\right)\left(\dfrac 1{R}-\dfrac 1{-R} \right)\\\implies \dfrac 1{f_a}=(0.5)\times \dfrac 2R\\\implies f_a=R..........(i)$$
But given the focal length of lens in air , $$f_a=10cm$$
Hence , $$R=10cm$$
Focal length in water can be calculated by the formula,
$$\dfrac 1{f_w}=\left(\dfrac {\mu_1}{\mu_2}-1\right)\left(\dfrac 1{R_1}-\dfrac 1{R_2} \right)\\\implies \dfrac 1{f_n}=\left(\dfrac {1.5}{\dfrac 43}-1\right)\left(\dfrac 1{R}-\dfrac 1{-R} \right)\\\implies \dfrac {1}{f_w}=\left(\dfrac {4.5}{4}-1\right)\left(\dfrac 2{R} \right)\\\implies\dfrac 1{f_w}=0.125\times \dfrac 2{10}\\\implies f_w=40cm$$
will be the focal length of the convex lens when immersed in water.
Question 5
1 / -0

Sodium lamps are used in foggy conditions because:

A
yellow light is scattered less by the fog particles

B
yellow light is scattered more by' the fog particles

C
yellow light is unaffected during its passage through the fog

D
Wavelength of yellow light is the mean of the visible part of the spectrum

Solution

The higher the wavelength the lesser the scattering. Yellow light has higher wavelength so it is least likely to be scattered among all colours in the visible region (except red & orange). So this light is visible from long distance even when there is foggy weather.
Question 6
1 / -0

Refraction occurs due to:

A
Change in direction of light

B
Change in speed of light

C
Change in quality of light

D
All

Solution

Refraction occurs due to change in optical properties of the light which causes change in direction and speed of light.

The light bends towards the normal or away from the normal if the refracting medium is denser or rarer respectively. The extent of bending is governed by Snell's law: $$\dfrac{n_i}{n_r}=\dfrac{sin \ \theta_r}{sin \ \theta_i}$$

The light slows down in a denser medium and becomes faster in a rarer medium.
Question 7
1 / -0

Which phenomena of light makes a pool of water appears to be less deep than it actually is?

A
Reflecion

B
Refraction

C
Diffraction

D
Lateral inversion

Solution

The rays of light coming from the bottom of the swimming pool travel from water to air. As the rays pass from denser medium (water) to rarer medium (air), they bend away from the normal. When the rays are produced back, they form an image of the bottom of the pool at a point above the real position. Therefore, the swimming pool appears to be less deep that it actually is.
This phenomenon takes place due to the refraction of light at the interface of the two media.

Hence, the correct answer is OPTION B.
Question 8
1 / -0

Why do high rise buildings have a red light on the top of the building?

A
Red light is the least scattered by fine particles

B
Red light can be easily spotted by the pilot

C
Both A and B

D
None

Solution

Red light is the least scattered by fine particles, fog or smoke present in the atmosphere which makes it easier to detect it clearly and distinctly so that pilot gets notification that there is some object and avoid from any collision.
Question 9
1 / -0

The sun appears red at the time of sun-rise and sun-set. This is because:

A
red colour is least scattered

B
red colour is most scattered

C
the sun is red in colour

D
our eyes can sense only red colour

Solution

Among the constituent colours of white light, red has the longest wavelength and hence least frequency. Scattering is inversely proportional to wavelength .As a result, red is least scattered among all colours. So, red colour reaches our eyes while all other colours scatter away during sun-rise and sun-set.
Question 10
1 / -0

Refractive index of diamond with respect to glass is $$1.6$$ and absolute refractive index of glass is $$1.5$$. Find out the absolute refractive index of diamond.

A
$$1.06$$

B
$$0.93$$

C
$$2.4$$

D
$$0.75$$

Solution

Given,

Refractive index of diamond with respect to glass, $${ _{ g }{ n }_{ d } } = 1.6$$,

Absolute refractive index of glass, $$n_{g} = 1.5$$

Refractive index of diamond with respect to glass $$= \dfrac {\text {Absolute refractive index of diamond}}{\text {Absolute refractive index of glass}}$$

Therefore, absolute refractive index of diamond $$=$$ Refractive index of diamond with respect to glass $$\times$$ Absolute refractive index of glass $$= 1.6 \times 1.5 = 2.4$$

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Ray Optics and Optical Test - 35

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Question 1

If both Assertion 'and Reason are correct and Reason is the correct explanation of Assertion

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

If Assertion is correct but Reason is incorrect

If Assertion is incorrect but Reason is correct

Solution

Question 2

all of

a part of

no

either all or no

Solution

Question 3

2R

$$\frac {2}{R}$$

4R

3R

Solution

Question 4

Both assertion and reason are true but the reason is the correct explanation of assertion

Both assertion and reason are true but the reason is not the correct explanation of assertion

Assertion is true but reason is false

Both the assertion and reason are false

Reason is true but assertion is false

Solution

Question 5

yellow light is scattered less by the fog particles

yellow light is scattered more by' the fog particles

yellow light is unaffected during its passage through the fog

Wavelength of yellow light is the mean of the visible part of the spectrum

Solution

Question 6

Change in direction of light

Change in speed of light

Change in quality of light

All

Solution

Question 7

Reflecion

Refraction

Diffraction

Lateral inversion

Solution

Question 8

Red light is the least scattered by fine particles

Red light can be easily spotted by the pilot

Both A and B

None

Solution

Question 9

red colour is least scattered

red colour is most scattered

the sun is red in colour

our eyes can sense only red colour

Solution

Question 10

$$1.06$$

$$0.93$$

$$2.4$$

$$0.75$$

Solution

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