Power of a Lens

Power of a Lens

Power of a Lens

Definition:

• The power of a lens is its capacity to deviate a ray. It is measured as the reciprocal of the focal length in meters, i.e., the SI unit of power: diopter (D).

Lens Power for Different Lenses:

• The power of a convex lens is positive, and the power of a concave lens is negative.

Power of Combination of Lenses:

• If two lenses are placed in contact, then the power of the combination is equal to the sum of the powers of the individual lenses.

Change in the Power of a Lens

If a lens is dipped in a liquid, its focal length and power both change. This change depends upon the refractive indices of the lens and the liquid.

The following situations are possible:

1. μ > μ' (Lens in a liquid with a smaller refractive index):

• For example, for a glass lens (μ = 1.5) dipped in water (μ = 1.33), the focal length of the lens increases, and the power of the lens decreases.

2. μ = μ' (Lens in a liquid with equal refractive index):

• The focal length of the lens becomes infinite, and the power of the lens becomes zero.

• The lens and the liquid behave as a single medium.

3. μ < μ' (Lens in a liquid with a higher refractive index):

• The focal length increases, the power decreases, and the nature of the lens changes.

• For example, a convex lens behaves as a concave lens when dipped in a liquid with a higher refractive index (e.g., carbon disulfide).

Formation of Images by Lenses

Dispersion of Light

Definition:

• Dispersion is the phenomenon where a ray of white light (or composite light) is passed through a prism and split into its constituent colors.

• This phenomenon is called the dispersion of light.

• The colored pattern obtained on a screen after dispersion of light is called the spectrum.

Cause of Dispersion:

• Dispersion occurs due to the different deviations suffered by different colors of light.

• The deviation is maximum for violet light and minimum for red light. The sequence of colors in the spectrum is

  • Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR).

Reason for Different Deviation:

• The dispersion of light is due to the different velocities of light in different colors.

• The refractive index of a medium is different for each color.

• The velocity of light is maximum for red light (with the lowest refractive index) and minimum for violet light (with the highest refractive index).

Rainbow

Definition:

• A rainbow is a colored display in the form of an arc seen in the sky, observed during or after a drizzle, appearing on the opposite side of the sun.

• The rainbow is formed due to the dispersion and refraction of sunlight by suspended water droplets.

Types of Rainbows:

• Primary Rainbow:

  • Formed due to two refractions and one total internal reflection of light falling on raindrops.

  • The order of colors in the primary rainbow has red on the convex side and violet on the concave side.

  • The angular width is 2°, and the average angle of elevation is 41°.

• Secondary Rainbow:

  • Formed due to two refractions and two internal reflections.

  • The color order is reversed, with violet on the convex side and red on the concave side.

  • The angular width is 3.5°, and the average angle of elevation is 52.75°.

  • The secondary rainbow is less intense than the primary one.

Theory of Colours

Color Perception:

• Color is the sensation perceived by the cones in the eye due to light.

Primary Colors:

• The spectral colors blue, green, and red are called primary colors because all other colors can be produced by mixing these in proper proportions:

  • Blue + Red + Green = White

Secondary Colors:

• A color produced by mixing any two primary colors is a secondary color. The three secondary colors are

  • Yellow (Green + Red),

  • Magenta (Red + Blue),

  • Cyan (Blue + Green).

  • Mixing all three secondary colors results in white:

    • Yellow + Magenta + Cyan = White

Complementary Colors:

• Two colors are complementary if their combination produces white light. The complementary pairs are:

  • Red and Cyan,

  • Blue and Yellow,

  • Green and magenta.

Colour of Bodies

The color of a body is the color of the light it reflects or transmits. An object appears white if it reflects all the components of white light, and it appears black if it absorbs all the incident light.

• Example Table for How Objects Appear Under Different Light:

Scattering of Light

Definition:

• Scattering occurs when light waves fall on small particles such as dust, water droplets, or suspended particles in a colloidal solution, causing them to scatter in all directions.

Effect of Scattering:

• The scattering of light is most intense for violet light and least for red light.

Examples of Scattering:

• Blue Sky: The blue color of the sky is due to the scattering of light.

• Red Sun: The brilliant red color of the rising and setting sun is due to the scattering of light.

Interference of Light

Definition:

• Interference occurs when two light waves of the same frequency and a constant phase difference travel in the same direction and superimpose.

• The resulting intensity is different from the sum of the intensities of the individual waves.

Types of Interference:

1. Constructive Interference: When two waves meet in phase, the resultant intensity is maximum.

2. Destructive Interference: When two waves meet in opposite phase, the resultant intensity is minimum.

Diffraction of Light

Definition:

• Diffraction occurs when light waves pass through a narrow opening or edge and spread out beyond the region of geometrical shadow.

Polarisation of Light

Definition:

• Polarization is the phenomenon that proves light is a transverse wave.

• Light is an electromagnetic wave in which electric and magnetic field vectors vibrate perpendicular to each other and the direction of propagation.

Effect of Polarization:

• In ordinary light, the vibrations of the electric field vector occur in every plane perpendicular to the direction of propagation.

• Polarization restricts the vibrations of light to a particular direction.

Final Thoughts

The power of a lens is a key concept in optics, explaining how light is bent to form images in tools like eyeglasses, cameras, and microscopes. It’s influenced by the focal length and the lens power, which together determine how light is refracted.

Dispersion of light also plays a role in phenomena like rainbows, showing how different colors bend at varying degrees.

Understanding these principles connects theoretical knowledge with real-world technology, helping us grasp everything from everyday devices to complex scientific concepts. Whether you're studying light behavior or using optics in daily life, these foundational ideas are crucial in advancing our understanding of modern technology and scientific exploration.