Ray Optics and Optical Test

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Ray Optics and Optical Test - 41

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Question 1
1 / -0

The object and the image are at distance of $$9\ cm$$ and $$16\ cm$$ respectively from the focal length of an equiconvex lens of radius of curvature $$12 \ cm$$. The refractive index of the material of the lens is:

A
1$$.45$$

B
$$1.5$$

C
$$1.55$$

D
$$1.6$$

Solution

Given: $$u=9\ cm$$ and $$v=16\ cm$$
Using Newton's formula, we can write the focal length of the lens as:
$$f=\sqrt{uv}$$
$$=\sqrt{9\times 16}\\ =12\ cm$$

Now, applying Lens maker's formula, we have
$$\Rightarrow \dfrac{1}{f}=(\mu -1)\dfrac{2}{R} $$

$$\Rightarrow \dfrac{1}{12}=(\mu -1)\dfrac{2}{12} $$ ....($$\because R=12\ cm$$)

$$\Rightarrow \dfrac{1}{12}=(\mu -1)\dfrac{1}{6} $$

$$\Rightarrow \dfrac{1}{2}=(\mu -1) $$

$$\Rightarrow \mu =1+\dfrac{1}{2} =1.5$$
Question 2
1 / -0

The refractive indices of glass and quartz w.r.t. air are 3/2 and 12/5 respectively. The refractive index of quartz w.r.t. glass is:

A
8/5

B
5/8

C
5/18

D
18/5

Solution

Given that, $$\displaystyle ^{ a }{ \mu }_{ g }=\frac { 3 }{ 2 } $$ and $$\displaystyle ^{ a }{ \mu }_{ q }=\frac { 12 }{ 5 } $$
So, we get
$$\displaystyle \therefore \quad ^{ g }{ \mu }_{ q }=\frac { { \mu }_{ q } }{ { \mu }_{ a } } .\frac { { \mu }_{ a } }{ { \mu }_{ g } } =\frac { { \mu }_{ q } }{ { \mu }_{ g } } $$
$$\displaystyle =\frac { 12 }{ 5 } \times \frac { 2 }{ 3 } =\frac { 8 }{ 5 } $$
Question 3
1 / -0

When a ray of light is refracted, the refracted ray does not have the same wavelength as the incident ray. Which of the following explain this phenomenon?
I. Some of the energy of the incident ray is carried away by the reflected ray
II. The boundary surface absorbs some of the energy of the incident ray
III. The incident and refracted rays do not travel with the same velocity

A
I only

B
II only

C
III only

D
I and II only

E
I, II, and III

Solution

Statement I is true, but it doesnt explain why a refracted ray should have a different wavelength. The fact that some of the incident ray is reflected means that the refracted ray will have a different amplitude, but it will not affect the frequency.
Statement II is false, and even if it were true, a change in energy would affect the frequency of the wave, not its wavelength.
Statement III correctly explains why refracted rays have different wavelengths from their incident rays. A light ray will maintain the same frequency, and hence color, when it is refracted. However, since the speed of light differs in different substances, and since the wavelength is related to the speed of light, v, by the formula $$\lambda=\dfrac{v}{f}$$ a change in the speed of light will make a change in the wavelength as well.
Question 4
1 / -0

The lateral shift in rectangular glass slab depends on which of the following properties of a medium ?

A
Refractive Index

B
Thickness

C
Colour

D
Both A and B

Solution

When light rays passed from the rarer medium of air to that of the thick glass slab then the refraction of light will occur and the it will deviate from it's usual way of movement and shift toward the line normal to the glass slab and when it leaves the slab it will deviate away from the line normal to that of the glass surface and thus we get the lateral shift in the light ray.

Lateral shift =$$\dfrac{t}{\cos r}\sin (i-r)$$where t is the thickness of the material and all other are having standard notation.

so lateral shift depends on Refractive Index and thickness.
Question 5
1 / -0

A persons image appears on the far side of an optical instrument, upside down. What is the optical instrument?

A
Concave mirror

B
Convex mirror

C
Plane mirror

D
Concave lens

E
Convex lens

Solution

Here the image is upside down means inverted so only concave mirror and convex lens create inverted image. But the concave mirror forms the inverted image same side of the object but here image is opposite side of the object. Thus, it should be convex lens.
Question 6
1 / -0

The main reason for axial chromatic aberration in the formation of images by a lens is/are:

A
focal length of lens is different for different colors.

B
the material used to make the lens is not uniform.

C
different sections of the lens are of different thickness.

D
all of the above.

Solution

Chromatic aberration, also known as “color fringing” or “purple fringing”, is a common optical problem that occurs when a lens is either unable to bring all wavelengths of color to the same focal plane, and/or when wavelengths of color are focused at different positions in the focal plane. Chromatic aberration is caused by lens dispersion, with different colors of light traveling at different speeds while passing through a lens. As a result, the image can look blurred or noticeable colored edges (red, green, blue, yellow, purple, magenta) can appear around objects, especially in high-contrast situations.
SO the maain reason is focal length of lens is different for different colors.
Question 7
1 / -0

For which of the two lenses $$L_1$$ and $$L_2$$ the chromatic aberration will be more if the power of $$L_1$$ is less than that of $$L_2$$:

A
$$L_1$$

B
$$L_2$$

C
$$L_1=L_2$$

D
none of the above

Solution

Power of L1 is less than L2 that means focal length of L1 is greator than L2,because-
$$f=\frac{1}{P}$$

and Chromatic aberration will be more for greator focal length.
Question 8
1 / -0

A magnifying glass is what kind of lens, and where do where should I place the lens relative to the object to see an image larger than the object and right-side-up? (f stands for the focal length of the lens.)

A
Type of Lens - convex, Location of Lens Relative to Object In terms of f - closer than f to object

B
Type of Lens - concave, Location of Lens Relative to Object In terms of f - closer than f to object

C
Type of Lens - convex, Location of Lens Relative to Object In terms of f - between f and $$2f$$ from object

D
Type of Lens - concave, Location of Lens Relative to Object In terms of f - between f and $$2f$$ from object

E
Type of Lens - convex, Location of Lens Relative to Object In terms of f - greater than $$2f$$ from object

Solution

When an object is placed between the pole and focus of the convex lens, then lens forms a virtual but erect and enlarged image of the object. Hence option A is correct.
Question 9
1 / -0

Refraction of light occurs when:

A
light passes through a narrow opening.

B
light passes into a new transparent material (not head on) in which it travels at a new speed.

C
light strikes the edge of an object.

D
light becomes polarized.

E
light passes through a diffraction grating.

Solution

When light ray goes from one transparent medium to another transparent medium it changes its path and travels with a new speed , this phenomenon is called refraction .
Question 10
1 / -0

In chromatic aberration of a convex lens, :

A
the image of a straight object becomes wavy.

B
the image of a white object become colored and blurred.

C
both A and B

D
none of the above

Solution

Chromatic aberration, also known as “color fringing” or “purple fringing”, is a common optical problem that occurs when a lens is either unable to bring all wavelengths of color to the same focal plane, and/or when wavelengths of color are focused at different positions in the focal plane. Chromatic aberration is caused by lens dispersion, with different colors of light travelling at different speeds while passing through a lens. As a result, the image can look blurred or noticeable colored edges (red, green, blue, yellow, purple, magenta) can appear around objects, especially in high-contrast situations.

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Ray Optics and Optical Test - 41

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Ray Optics and Optical Test - 41

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Question 1

1$$.45$$

$$1.5$$

$$1.55$$

$$1.6$$

Solution

Question 2

8/5

5/8

5/18

18/5

Solution

Question 3

I only

II only

III only

I and II only

I, II, and III

Solution

Question 4

Refractive Index

Thickness

Colour

Both A and B

Solution

Question 5

Concave mirror

Convex mirror

Plane mirror

Concave lens

Convex lens

Solution

Question 6

focal length of lens is different for different colors.

the material used to make the lens is not uniform.

different sections of the lens are of different thickness.

all of the above.

Solution

Question 7

$$L_1$$

$$L_2$$

$$L_1=L_2$$

none of the above

Solution

Question 8

Type of Lens - convex, Location of Lens Relative to Object In terms of f - closer than f to object

Type of Lens - concave, Location of Lens Relative to Object In terms of f - closer than f to object

Type of Lens - convex, Location of Lens Relative to Object In terms of f - between f and $$2f$$ from object

Type of Lens - concave, Location of Lens Relative to Object In terms of f - between f and $$2f$$ from object

Type of Lens - convex, Location of Lens Relative to Object In terms of f - greater than $$2f$$ from object

Solution

Question 9

light passes through a narrow opening.

light passes into a new transparent material (not head on) in which it travels at a new speed.

light strikes the edge of an object.

light becomes polarized.

light passes through a diffraction grating.

Solution

Question 10

the image of a straight object becomes wavy.

the image of a white object become colored and blurred.

both A and B

none of the above

Solution

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