Thin Lenses MCQ Quiz - Objective Question with Answer for Thin Lenses - Download Free PDF

Calculation:

Location of image of A :-

(1/v) - (1/u) = (1/f)

⇒ (1/v) - (1/(v - 30)) = (1/20)

⇒ (1/v) = (1/60)

⇒ v = 60 cm

The magnification m = 2.

Since the size of the object is small with respect to the location, hence

dv = m² du ⇒ dv = 4 × 1 = 4 cm

h_i = m h₀ ⇒ h_i(dy) = 2 × 2 = 4 cm

Therefore, Angle made with principle a×is = -45°

Calculation:
For series combination of lens:

p_eff = p₁ + p₂ + p₃ + p₄ = 4p

m_eff = m₁ × m₂ × m₃ × m₄ = m⁴

Applying lens maker formula for lens 1,

\(\dfrac{1}{f_{1}} = (\mu - 1)\left( \dfrac{1}{R_{1}}- \dfrac{1}{R_{2}}\right)\)

\(\dfrac{1}{f_{1}} = (1.5 - 1)\left( \dfrac{1}{14}-0\right)\)

\(\dfrac{1}{f_{1}}= \dfrac{0.5}{14}\)

For lens 2,

\(\dfrac{1}{f_{2}} = (\mu - 1)\left( \dfrac{1}{R_{1}}- \dfrac{1}{R_{2}}\right)\)

\(\dfrac{1}{f_{2}} = (1.2 - 1)\left( 0- \left(\dfrac{1}{-14}\right)\right)\)

\(\dfrac{1}{f_{2}}= \dfrac{0.2}{14}\)

Now,

\(\dfrac{1}{f}= \dfrac{1}{f_{1}} + \dfrac{1}{f_{2}}\)

so \(\dfrac{1}{f}= \dfrac{0.7}{14}\)

Therefore, From lens formula :

\(\dfrac{1}{v}= \dfrac{7}{140} - \dfrac{1}{40}\)

v=40 cm

Explanation:

Two plano-convex lens of focal length \( f \), when combined will give rise to a convex lens of focal length \( \frac{f}{2} \).

The image will be of same size if object is placed at \( 2f \) i.e.

At a distance \( f \) from optical centre.

Calculation:

\(\frac{1}{8}=\left(\frac{\mu_{\ell}}{\mu_{\mathrm{s}}}-1\right)\left[\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right] \)

\(\frac{1}{24}=(1.5-1)\left[\frac{2}{\mathrm{R}}\right] \)

\(\frac{1}{\mathrm{f}^{\prime}}=\left(\frac{1.5}{1.33}-1\right)\left(\frac{2}{\mathrm{R}}\right) \)

\(\frac{1}{\mathrm{f}^{\prime}}=\left(\frac{1.5 \times 3}{4}-1\right) \frac{2}{\mathrm{R}}\)

(i) divided by (ii)

\(\frac{\mathrm{f}^{\prime}}{24}=4\)

∴ f' = 96 cm

CONCEPT:

• Power of the Lens: The lens power is the inverse of the focal length in meters.
  • The physical unit for lens power is 1/meter which is called dioptre (D).

Power (P) = 1/f 

Where f is the focal length of the lens

CALCULATION:

Given that:

Focal length of the lens (f) = 1 cm = 1/100 = 0.01 m

So the power of the lens, \(p\; = \;\frac{1}{{f}}\; = \;\frac{1}{0.01}\; = \;100\;D\)

Option 2 is the correct answer: 

CONCEPT:

• Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
• Concave lens: It is a diverging lens that diverges the parallel beam of light.
  • It can also gather light from all directions and project it as a parallel beam.
  • It has a virtual focus from the diverging rays of light that seem to converge.
  • The image formed by a concave lens is virtual, erect, and diminished.

The lens equation which gives the relation between focal length, the distance of image and object from the lens is

\({1 \over f} = {{1 \over v }-{1 \over u}}\)

where f is the focal length, u is the distance of the object from the lens and v is that of the image from the lens.

CALCULATION:

• The focal length of a concave lens is taken negative (is measured opposite to the incident rays).

Given that:

focal length f = -15 cm

Distance of object u = - 30 cm

\({1 \over v} = {{1 \over f }+{1 \over u}}\)

substituting these values in the lens equation we get,

\({1 \over v} = {-{1 \over 15}-{1 \over 30}}\)

\({1 \over v}={-2-1 \over 30}\)

\({1 \over v}={-3 \over 30}\)

\(v=-10cm\)

Hence distance of the object from the lens is 10 cm and the negative sign signifies a virtual image. So option 2 is correct.

EXTRA POINTS:

Positions of the object and image for the concave lens:

Concept:

• The focal length of a combination of lenses is calculated by:

\(\frac{1}{f} = \frac{1}{f_1} +\frac{1}{f_2}\)

Calculation:

Given f₁ = + 50 cm (For convex lens) and f₂ = - 40cm (For concave lens)

\(\frac{1}{f} = \frac{1}{50} + \frac{1}{-40}\)

\( ⇒\frac{1}{f} = \frac{4-5}{200}\)

\( ⇒ \frac{1}{f} = -\frac{1}{200}\)

⇒ \(f = - 200\ cm\)

• Since focal length is negative therefore the combination of the lens is a diverging lens of 200 cm focal length.

 Additional Information

Power is reciprocal to focal length.

\(P = \frac{1}{f}\)

The correct answer is the Concave lens.

Key Points

• Myopia
  • It is an eye disorder of near-sightedness.
  • In myopia, light focuses in front of, instead of on, the retina.
  • This makes distant objects blurry and close objects appear normal.
• Concave lens
  • A concave lens is a lens that possesses at least one surface that curves inwards.
  • It is a diverging lens
  • It is thinner at its centre than at its edges.
  • Uses of Concave lens - in telescopic, in Eye Glasses, etc.

Additional Information

• Convex lens
  • It is a lens that converges rays of light that are travelling parallel to its principal axis.
  • It is a converging lens.
  • It is thicker at the centre and thinner at the edges.
  • It is used to correct Hypermetropia, used in cameras.
• Cylindrical lens
  • A cylindrical lens is a lens that focuses light into a line instead of a point
  • The lens compresses the image in a direction perpendicular to this line.
  • Cylindrical lenses are used in optical spectrometers.
  • It is used in holography.

CONCEPT:

• The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
• The lens whose refracting surface is upside is called a convex lens and the lens whose refracting surface is inside is called a concave lens or diverging lens.
  • Concave lenses diverge light rays and hence are also called diverging lenses.

Positions of the object and image:

EXPLANATION:

• When the object is between the infinity and optical center of the lens then the image forms between focus and optical center which is diminished, virtual and erect. So option 1 is correct.

CONCEPT:

• Power of Lens: The inverse of the focal length is known as the power of the lens.
  • It shows the bending strength for the light ray of the lens.
  • The unit of power of a lens is Dioptre when the focal length of the lens is taken in meter (m).

\(P = \frac{1}{f}\)

where P is the power of the lens and f is the focal length of the lens.

• Concave lens: It is a diverging lens that diverges the parallel beam of light.
  • It can also gather light from all directions and project it as a parallel beam.
  • The focal length of the concave lens is negative.
  • It has a virtual focus from the diverging rays of light that seem to converge.
• Convex lens: The lens whose refracting surface is upside is called a convex lens.
  • The convex lens is also called a converging lens.
  • The focal length of a convex lens is positive.

CALCULATION:

Focal length (f) = 50 cm = 50/100 = 0.5 m

Since f = 1/P 

So power of the lens (P) = 1/f = 1/0.5 = 2 D

The focal length of a convex lens is positive. 

So the correct answer is option 3.

CONCEPT:

• Power of Lens: The inverse of the focal length is known as the power of the lens.
  • It shows the bending strength for the light ray of the lens.
  • The unit of power of a lens is Dioptre when the focal length of the lens is taken in meter (m).

\(P = \frac{1}{f}\)

where P is the power of the lens and f is the focal length of the lens.

• Concave lens: It is a diverging lens that diverges the parallel beam of light.
  • It can also gather light from all directions and project it as a parallel beam.
  • The focal length of the concave lens is negative.
  • It has a virtual focus from the diverging rays of light that seem to converge.
• Convex lens: The lens whose refracting surface is upside is called a convex lens.
  • The convex lens is also called a converging lens.
  • The focal length of a convex lens is positive.

CALCULATION:

Given that P = 1.5 D 

Focal length (f) = 1/P = 1/(1.5) = 1/1.5 = 0.666 m = 66.6 cm

The focal length of a convex lens is positive.

So the correct answer is option 2.

CONCEPT:

• The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
  • The lens whose refracting surface is upside is called a convex lens.
  • The convex lens is also called a converging lens.

Lens formula is given by:

\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)

Where u is object distance, v is image distance and f is the focal length of the lens

CALCULATION:

Given that: 

Object distance (u) = - 20 cm

Focal length (f) = 7.5 cm

Use the lens formula:

 \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)

\(\frac{1}{v} - \frac{1}{-20} = \frac{1}{7.5}\)

\(\frac{1}{v} = \frac{1}{7.5} - \frac{1}{20} =\frac{20-7.5}{7.5\times 20}=\frac{12.5}{150}\)

So image distance (v) = 150/12.5 = 12 cm

Hence option 3 is correct.

Concept:

There are mainly 2 types of lenses:

Concave lens:

• It is a type of lens that possess at least one surface that is curved inside.
• It is also known as the diverging lens.

The characteristics of an image formed in a Concave Lens:

• The concave lens is thinner in the middle and thicker at the edge.
• The image formed by a concave lens is always upright, virtual, and erect.
• The size of the image is always smaller than the object.
• The image can be found between the focus and the lens.
• The focal length is always negative.

Convex Lens:

• It is a type of lens that possess at least one surface which curves outside much similar to the exterior of a sphere.
• It is also known as a converging mirror.

The characteristics of an image formed in a Convex Lens:

• ​A convex lens is thicker in the middle and thinner at the edge.
• Depending on the point of the object:     
  • The image may be real or virtual.
  • image may be erect or inverted.
  • image may be magnified or diminished.

Explanation:

• A concave lens diverges incoming light rays and always produces an upright, diminished and virtual, and erect image of the object in front of it.

Image formation by the concave lens:

Thus, from the above discussion, we can say that the correct answer is It is upright and smaller than the object.

CONCEPT:

• Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
  • Convex lens: The lens whose refracting surface is upside is called a convex lens.
  • The convex lens is also called a converging lens.

Lens formula is given by:

\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)

Where u is object distance, v is image distance and f is the focal length of the lens

CALCULATION:

Given that: 

Object distance (u) = - 20 cm

Focal length (f) = 7.5 cm

Use 

\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)

\(\frac{1}{v} - \frac{1}{-20} = \frac{1}{7.5}\)

\(\frac{1}{v} =- \frac{1}{20} + \frac{1}{7.5} =1/12\)

So v = 12 cm.

Hence option 3 is correct.