Optical Instruments MCQ Quiz - Objective Question with Answer for Optical Instruments - Download Free PDF

Calculation:

Objective focal length (f_o) = 2 cm

Eyepiece focal length (f_e) = 4 cm

Tube length (L) = 40 cm

Distance of distinct vision of eye (D) = 25 cm

Formula for magnification (m) of the microscope:

m = (L / f_o) × (D / f_e)

⇒ m = (40 / 2) × (25 / 4)

⇒ m = 125

Final Answer: The magnification in the microscope is 125.

The correct answer is: Option 1) 27°

Concepts:

An astronomical telescope forms an image of a distant object by using an objective lens and an eyepiece lens. The angular magnification (M) of a telescope when the final image is formed at the least distance of distinct vision (D) can be given by:

M = (f_O / f_E) × (1 + f_E / D)

where f_O is the focal length of the objective and f_E is the focal length of the eyepiece. The angular size of the image is the product of the angular magnification and the angular size of the object.

Calculation:

Given:

f_O = 50 cm

f_E = 2 cm

D = 25 cm

Angular diameter of moon at the objective = 1/2°

First, calculate the angular magnification (M):

M = (50 / 2) × (1 + 2 / 25)

M = 25 × (1 + 0.08)

M = 25 × 1.08 = 27

Then, the angular size of the image = M × angular diameter of moon

Angular size of image = 27 × (1/2)°

Angular size of image = 13.5°

The correct answer is - (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Key Points

• Human eye (A)-(III)
  • The human eye uses a lens of adjustable focal length to focus light on the retina.
  • This lens adjusts to focus on objects at different distances, enabling clear vision.
• Microscope (B)-(II)
  • A microscope generally employs an objective lens of large aperture and large focal length to gather and focus light from the specimen.
  • This allows for the magnification and detailed observation of small objects.
• Reflecting telescope (C)-(I)
  • A reflecting telescope uses a concave mirror of large aperture and large focal length to collect and focus light from distant celestial objects.
  • This design helps to minimize chromatic aberration.
• Refracting telescope (D)-(IV)
  • A refracting telescope utilizes an objective of small aperture and small focal length to focus light, providing clear images of distant objects.
  • This type of telescope is known for its simplicity and ease of use.

Additional Information

• Human Eye
  • The lens in the human eye is flexible, allowing it to change shape to focus light on the retina.
  • This process is known as accommodation and is vital for clear vision at various distances.
• Microscope
  • Microscopes often have multiple objective lenses with varying focal lengths to provide different levels of magnification.
  • The large aperture helps in gathering more light, which is essential for viewing fine details in specimens.
• Reflecting Telescope
  • Reflecting telescopes are preferred in astronomy due to their ability to avoid chromatic aberration, which is common in refracting telescopes.
  • The large aperture of the concave mirror allows for the collection of more light, making it possible to observe faint celestial objects.
• Refracting Telescope
  • Refracting telescopes use lenses to bend light and focus it to form an image.
  • These telescopes are known for their straightforward design and are often used for terrestrial and celestial observations.

Concept:

• Secondary Mirror in a Reflecting Telescope:
• A secondary mirror in a reflecting telescope is used to redirect the light from the primary mirror to the eyepiece or camera.
• In many telescopes, the secondary mirror is essential for:
  • Making the design compact by moving the eyepiece outside the telescopic tube.
  • Allowing the telescope to have a large focal length in a shorter tube.
• The primary mirror of the telescope gathers the light and reflects it toward the secondary mirror, which then redirects the light to the eyepiece or camera.

Explanation:

The secondary mirror in a reflecting telescope serves the purpose of redirecting the light gathered by the primary mirror towards the eyepiece. This design allows for a compact telescope while maintaining a long focal length.

∴ The secondary mirror is used to move the eyepiece outside the telescopic tube.

Concept:

Power Delivered and Dissipated in a Transmission Cable:

• The power P delivered by a transmission cable with resistance R_e and voltage V is given by:
  • P = V² / R_e
• The power dissipated in the cable is given by:
  • P_diss = I² * R_c
• Where I is the current flowing through the cable and R_c is the resistance of the cable.
• Using the relation P = I² * R_e, we find:
  • I² = P / R_e
• Substitute this into the formula for power dissipated to find the final relationship:
  • P_diss = P² * R_c / V²
     

∴ The power dissipated is P² * R_c / V². Option 4) is correct.

Concept:

​Astronomical Telescope:

• It is used to observe distinct images of heavenly bodies.
• It consists of 2 lenses, the objective lens O with a large focal length and large aperture, and the eyepiece E which has a small focal length and small aperture.
• In the normal adjustment of the telescope, the final image is formed at infinity.

• 
• The angular magnification, \(m=\frac{f_0}{f_e}\)
• The distance between the objective focal length and the eyepiece focal length is, L = fe + f₀
• Here, f₀ = focal length of the objective lens, f_e = focal length of the eyepiece

Calculation:

Given,

The length of the astronomical telescope, L = 20 cm

Angular magnification,  m = 4

magnification, \(m=\frac{f_0}{f_e}\)

\(4=\frac{f_0}{f_e}\)

f₀ = 4f_e . . . . . . . . . . .(1)

The distance between the objective focal length and the eyepiece focal length is, L = f_e + f₀ . . . . . .(2)

Substitute the value of the f₀ in equation (2), and we get

L = 4f_e + f_e 

L = 5f_e

\(f_e=\frac{L}{5}\)

\(f_e=\frac{20}{5}=4cm\)

From equation (1),

f₀ = 4 × 4 = 16 cm

Calculation:

Objective focal length (f_o) = 2 cm

Eyepiece focal length (f_e) = 4 cm

Tube length (L) = 40 cm

Distance of distinct vision of eye (D) = 25 cm

Formula for magnification (m) of the microscope:

m = (L / f_o) × (D / f_e)

⇒ m = (40 / 2) × (25 / 4)

⇒ m = 125

Final Answer: The magnification in the microscope is 125.

Calculation: 

Magnification of compound microscope for least distance of distinct vision setting (strained eye)

M = (L/f0)(1 + (D/fe))

where L is the tube length

f0 is the focal length of objective

D is the least distance of distinct vision = 25 cm

⇒\(375=\frac{150 \times 10^{-3}}{5 \times 10^{-3}}\left(1+\frac{25 \times 10^{-2}}{f_e}\right)\)

⇒\(12.5=\left(1+\frac{25 \times 10^{-2}}{f_e}\right) \)

⇒\(\frac{25 \times 10^{-2}}{f_e}=11.5\)

⇒ fe ≈ 21.7 × 10−3m = 22 mm

∴ The Correct answer is Option (1): 22 mm

Concept:

​Astronomical Telescope:

• It is used to observe distinct images of heavenly bodies.
• It consists of 2 lenses, the objective lens O with a large focal length and large aperture, and the eyepiece E which has a small focal length and small aperture.
• In the normal adjustment of the telescope, the final image is formed at infinity.

• 
• The angular magnification, \(m=\frac{f_0}{f_e}\)
• The distance between the objective focal length and the eyepiece focal length is, L = fe + f₀
• Here, f₀ = focal length of the objective lens, f_e = focal length of the eyepiece

Calculation:

Given,

The length of the astronomical telescope, L = 20 cm

Angular magnification,  m = 4

magnification, \(m=\frac{f_0}{f_e}\)

\(4=\frac{f_0}{f_e}\)

f₀ = 4f_e . . . . . . . . . . .(1)

The distance between the objective focal length and the eyepiece focal length is, L = f_e + f₀ . . . . . .(2)

Substitute the value of the f₀ in equation (2), and we get

L = 4f_e + f_e 

L = 5f_e

\(f_e=\frac{L}{5}\)

\(f_e=\frac{20}{5}=4cm\)

From equation (1),

f₀ = 4 × 4 = 16 cm

Concept:

Types of Reflecting Telescopes with Secondary Mirrors
Newtonian Telescope
The primary mirror is parabolic and reflects light to a focal point inside the telescope tube.
A flat secondary mirror, called a diagonal, is placed at a 45° angle to the incoming light path. It reflects the light to the side of the telescope tube where the eyepiece or camera is located.
This configuration allows for a more compact design and is common in amateur telescopes.
Cassegrain Telescope
The primary mirror is parabolic or hyperbolic and focuses light back towards the mirror.
A convex secondary mirror is placed in the path of the converging light. It reflects the light back through a hole in the center of the primary mirror to an eyepiece or detector behind the primary mirror.

Calculation:

Here the secondary mirror is used to move the eyepiece outside the telescope & it has advantage of a large focal length in a short telescope.

∴ Option (3) is correct.

Concept:

​Astronomical Telescope:

• It is used to observe distinct images of heavenly bodies.
• It consists of 2 lenses, the objective lens O with a large focal length and large aperture, and the eyepiece E which has a small focal length and small aperture.
• In the normal adjustment of the telescope, the final image is formed at infinity.

• 
• The angular magnification, \(m=\frac{f_0}{f_e}\)
• The distance between the objective focal length and the eyepiece focal length is, L = fe + f₀
• Here, f₀ = focal length of the objective lens, f_e = focal length of the eyepiece
• The relation between the focal length f and power P is given as, \(P=\frac{1}{f}\)

Calculation:

Given,

The power of the objective lens, P_o = 0.5 D

The power of eyepiece, P_e = 20 D

magnification, \(m=\frac{f_0}{f_e} \)

\(m=\frac{P_e}{P_o}\)

\(m=\frac{20}{0.5}=40\)

The correct answer is - (A)-(III), (B)-(II), (C)-(I), (D)-(IV)

Key Points

• Human eye (A)-(III)
  • The human eye uses a lens of adjustable focal length to focus light on the retina.
  • This lens adjusts to focus on objects at different distances, enabling clear vision.
• Microscope (B)-(II)
  • A microscope generally employs an objective lens of large aperture and large focal length to gather and focus light from the specimen.
  • This allows for the magnification and detailed observation of small objects.
• Reflecting telescope (C)-(I)
  • A reflecting telescope uses a concave mirror of large aperture and large focal length to collect and focus light from distant celestial objects.
  • This design helps to minimize chromatic aberration.
• Refracting telescope (D)-(IV)
  • A refracting telescope utilizes an objective of small aperture and small focal length to focus light, providing clear images of distant objects.
  • This type of telescope is known for its simplicity and ease of use.

Additional Information

• Human Eye
  • The lens in the human eye is flexible, allowing it to change shape to focus light on the retina.
  • This process is known as accommodation and is vital for clear vision at various distances.
• Microscope
  • Microscopes often have multiple objective lenses with varying focal lengths to provide different levels of magnification.
  • The large aperture helps in gathering more light, which is essential for viewing fine details in specimens.
• Reflecting Telescope
  • Reflecting telescopes are preferred in astronomy due to their ability to avoid chromatic aberration, which is common in refracting telescopes.
  • The large aperture of the concave mirror allows for the collection of more light, making it possible to observe faint celestial objects.
• Refracting Telescope
  • Refracting telescopes use lenses to bend light and focus it to form an image.
  • These telescopes are known for their straightforward design and are often used for terrestrial and celestial observations.

Calculation:

Objective focal length (f_o) = 2 cm

Eyepiece focal length (f_e) = 4 cm

Tube length (L) = 40 cm

Distance of distinct vision of eye (D) = 25 cm

Formula for magnification (m) of the microscope:

m = (L / f_o) × (D / f_e)

⇒ m = (40 / 2) × (25 / 4)

⇒ m = 125

Final Answer: The magnification in the microscope is 125.

The correct answer is: Option 1) 27°

Concepts:

An astronomical telescope forms an image of a distant object by using an objective lens and an eyepiece lens. The angular magnification (M) of a telescope when the final image is formed at the least distance of distinct vision (D) can be given by:

M = (f_O / f_E) × (1 + f_E / D)

where f_O is the focal length of the objective and f_E is the focal length of the eyepiece. The angular size of the image is the product of the angular magnification and the angular size of the object.

Calculation:

Given:

f_O = 50 cm

f_E = 2 cm

D = 25 cm

Angular diameter of moon at the objective = 1/2°

First, calculate the angular magnification (M):

M = (50 / 2) × (1 + 2 / 25)

M = 25 × (1 + 0.08)

M = 25 × 1.08 = 27

Then, the angular size of the image = M × angular diameter of moon

Angular size of image = 27 × (1/2)°

Angular size of image = 13.5°

Concept:

• Secondary Mirror in a Reflecting Telescope:
• A secondary mirror in a reflecting telescope is used to redirect the light from the primary mirror to the eyepiece or camera.
• In many telescopes, the secondary mirror is essential for:
  • Making the design compact by moving the eyepiece outside the telescopic tube.
  • Allowing the telescope to have a large focal length in a shorter tube.
• The primary mirror of the telescope gathers the light and reflects it toward the secondary mirror, which then redirects the light to the eyepiece or camera.

Explanation:

The secondary mirror in a reflecting telescope serves the purpose of redirecting the light gathered by the primary mirror towards the eyepiece. This design allows for a compact telescope while maintaining a long focal length.

∴ The secondary mirror is used to move the eyepiece outside the telescopic tube.