Karnataka Board PUCPUC Science 2nd PUC Class 12

Does Focal Length of a Lens Depend on the Colour of the Light Used? Does Focal Length of a Mirror Depend on the Colour? - Physics

Short Note

Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?



Yes, the focal length of a lens depends on the colour of light.

According to lens-maker's formula,

\[\frac{1}{f} = (\mu - 1)(\frac{1}{R_1} - \frac{1}{R_2})\]

Here, f is the focal length, μ is the refractive index, R is the radius of curvature of lens.

The refractive index (μ) depends on the inverse of square of wavelength.

The focal length of a mirror is independent of the colour of light.

Concept: Lenses
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Chapter 20: Dispersion and Spectra - Short Answers [Page 441]


HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 20 Dispersion and Spectra
Short Answers | Q 5 | Page 441

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A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.

A biconvex lens made of glass (refractive index 1.5) has two spherical surfaces having radii 20 cm and 30 cm. Calculate its focal length.

What type of lens is used to correct long-sightedness?

What is the chromatic aberration? How can it be minimised or eliminated?

Under what condition does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid?

A convex lens of refractive index 1.5 has a focal length of 18 cm in air .Calculate the change in its focal length when it is immersed in water of refractive index `4/3`.

The maximum focal length of the eye-lens of a person is greater than its distance from the retina. The eye is

The focal length of a converging lens are fv and fr for violet and red light respectively.

In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit ___________ .

A person is viewing an extended object. If a converging lens is placed in front of his eyes, will he feel that the size has increased?

By mistake, an eye surgeon puts a concave lens in place of the lens in the eye after a cataract operation. Will the patient be able to see clearly any object placed at any distance?

An object is placed at a distance of 30 cm from a converging lens of focal length 15 cm. A normal eye (near point 25 cm, far point infinity) is placed close to the lens on the other side. (a) Can the eye see the object clearly? (b) What should be the minimum separation between the lens and the eye so that the eye can clearly see the object? (c) Can a diverging lens, placed in contact with the converging lens, help in seeing the object clearly when the eye is close to the lens?

A farsighted person cannot see objects placed closer to 50 cm. Find the power of the lens needed to see the objects at 20 cm.

A nearsighted person cannot clearly see beyond 200 cm. Find the power of the lens needed to see objects at large distances.

A professor reads a greeting card received on his 50th birthday with + 2.5 D glasses keeping the card 25 cm away. Ten years later, he reads his farewell letter with the same glasses but he has to keep the letter 50 cm away. What power of lens should he now use?

The near point and the far point of a child are at 10 cm and 100 cm. If the retina is 2.0 cm behind the eye-lens, what is the range of the power of the eye-lens?

A person has near point at 100 cm. What power of lens is needed to read at 20 cm if he/she uses (a) contact lens, (b) spectacles having glasses 2.0 cm separated from the eyes?

Lenses are constructed by a material of refractive index 1.50. The magnitude of the radii of curvature are 20 cm and 30 cm. Find the focal lengths of the possible lenses with the above specifications.

Calculate the focal length of a convex lens whose radii of curvature of two surfaces is 10 cm and 15 cm respectively and its refractive index is 1.5. 

What is meant by shortsightedness?

What is meant by short-sightedness ?

When two thin lenses of focal lengths f1 and f2 are kept coaxially and in contact, prove that their combined focal length ‘f’ is given by: `1/f = 1/f_1 + 1/f_2`

 Show that, two thin lenses kept in contact, form an achromatic doublet if they satisfy the condition: `ω/f + (w')/(f') = 0`
where the terms have their usual meaning.

Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of -5D? 

Can the optical centre of a lens be situated outside the lens?

Read the following paragraph and answer the questions that follow.

Types of Lenses and their combination

     A convex or converging lens is thicker at the centre than at the edges. It converges a beam of light on refraction through it. It has a real focus. Convex lens is of three types: Double convex lens, Plano-convex lens and Concavo-convex lens.

The concave lens is thinner at the centre than at the edges. It diverges a beam of light on refraction through it. It has a virtual focus. Concave lenses are of three types: Double concave lens, Plano concave lens and Convexo-concave lens.

When two thin lenses of focal lengths f1 and f2 are placed in contact with each other along their common principal axis, then the two-lens system is regarded as a single lens of focal length f and `1/f = 1/f_1 + 1/f_2`
If several thin lenses of focal length f1, f2, .... fn are placed in contact, then the effective focal length of the combination is given by `1/f = 1/f_1 + 1/f_2 + ... + 1/f_n`
and in terms of power, we can write P = P1 + P2 + ... + Pn

The value of focal length and power of a lens must be used with proper sign consideration.

  1. Two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, the focal length of the other would be ______.
    (a) -26.7 cm
    (b) 60 cm
    (c) 80 cm
    (d) 30 cm
  2. A spherical air bubble is embedded in a piece of glass. For a ray of light passing through the bubble, it behaves like a ______.
    (a) converging lens
    (b) diverging lens
    (c) mirror
    (d) thin plane sheet of glass
  3. The lens generally used in magnifying glasses is ______.
    (a) single concave lens
    (b) single convex lens
    (c) combination of a convex lens of lower power and a concave lens of lower focal length
    (d) Planoconcave lens
  4. The magnification of an image by a convex lens is positive only when the object is placed ______.
    (a) at its focus F
    (b) between F and 2F
    (c) at 2F
    (d) between F and the optical centre
    A convex lens of 20 cm focal length forms a real image which is three times magnified. The distance of the object from the lens is ______.
    (a) 13.33 cm
    (b) 14 cm
    (c) 26.66 cm
    (d) 25 cm

Read the passage given below and answer the questions that follow.

There are two types of lenses: Converging lenses and diverging lenses, depending on whether they converge or diverge an incident beam of light. They are also called convex or concave lenses. Lenses are usually made of glass. Convex lenses are more popular as they form a real image of an object. They are widely used in our daily life, for instance, in microscopes, telescopes, projectors, cameras, spectacles, etc. Microscopes are used to view small and nearby objects, whereas telescopes are used to see distant objects.
  1. State any one factor on which the focal length of a lens depends.
  2. Give an example where a convex lens behaves like a diverging lens.
  3. What type of lens is used in a camera?
  4. Write an expression for magnifying power of a compound microscope when its final image lies at the least distance of distinct vision (D).
  5. State any one difference between a reflecting telescope and a refracting telescope.


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