krit.club logo

Physics - Light Energy (Refraction, Lenses, Dispersion)

Grade 8ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Refraction is the change in direction (bending) of light when it passes obliquely from one transparent medium to another due to a change in its speed. Light travels at c=3×108 m/sc = 3 \times 10^8 \text{ m/s} in vacuum.

•

Laws of Refraction: 1. The incident ray, refracted ray, and the normal at the point of incidence all lie in the same plane. 2. Snell's Law states that the ratio of the sine of the angle of incidence ii to the sine of the angle of refraction rr is constant for a given pair of media, represented as sin⁡isin⁡r=μ\frac{\sin i}{\sin r} = \mu.

•

Optical Density: A medium in which the speed of light is less is called an optically denser medium, and one where the speed of light is more is called an optically rarer medium. Light bends towards the normal when moving from rarer to denser media.

•

Real and Apparent Depth: Objects underwater appear to be at a shallower depth than they actually are due to refraction. This is governed by the refractive index μ\mu.

•

Lenses: A Convex Lens (Converging) is thicker in the middle and converges parallel rays to a point called the Principal Focus FF. A Concave Lens (Diverging) is thinner in the middle and diverges parallel rays so they appear to come from the focus.

•

Dispersion: The phenomenon of splitting white light into its seven constituent colors (VIBGYORVIBGYOR) when passing through a glass prism. Red light deviates the least, while Violet light deviates the most because μviolet>μred\mu_{violet} > \mu_{red}.

•

Total Internal Reflection (TIR): Occurs when light travels from a denser to a rarer medium and the angle of incidence is greater than the Critical Angle CC.

📐Formulae

μ=Speed of light in vacuum (c)Speed of light in medium (v)\mu = \frac{\text{Speed of light in vacuum (c)}}{\text{Speed of light in medium (v)}}

Refractive Index (μ)=Real DepthApparent Depth\text{Refractive Index (}\mu\text{)} = \frac{\text{Real Depth}}{\text{Apparent Depth}}

sin⁡isin⁡r=μ\frac{\sin i}{\sin r} = \mu

P=1f (in meters)P = \frac{1}{f \text{ (in meters)}}

1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

💡Examples

Problem 1:

If the speed of light in a glass slab is 2×108 m/s2 \times 10^8 \text{ m/s} and the speed of light in vacuum is 3×108 m/s3 \times 10^8 \text{ m/s}, calculate the refractive index of glass.

Solution:

Given c=3×108 m/sc = 3 \times 10^8 \text{ m/s} and v=2×108 m/sv = 2 \times 10^8 \text{ m/s}. Using μ=cv\mu = \frac{c}{v}, we get μ=3×1082×108=1.5\mu = \frac{3 \times 10^8}{2 \times 10^8} = 1.5.

Explanation:

The refractive index is a dimensionless ratio that indicates how much the light slows down in the medium compared to vacuum.

Problem 2:

A swimming pool appears to be 3 m3 \text{ m} deep. If the refractive index of water is 1.331.33 (or 43\frac{4}{3}), find the actual depth of the pool.

Solution:

μ=Real DepthApparent Depth\mu = \frac{\text{Real Depth}}{\text{Apparent Depth}}. Therefore, 1.33=Real Depth31.33 = \frac{\text{Real Depth}}{3}. Real Depth =1.33×3=3.99≈4 m= 1.33 \times 3 = 3.99 \approx 4 \text{ m}.

Explanation:

Refraction makes the bottom of the pool appear closer to the surface than it actually is.

Problem 3:

Calculate the power of a convex lens with a focal length of 20 cm20 \text{ cm}.

Solution:

First, convert focal length to meters: f=20100=0.2 mf = \frac{20}{100} = 0.2 \text{ m}. Using P=1fP = \frac{1}{f}, we get P=10.2=+5 DP = \frac{1}{0.2} = +5 \text{ D}.

Explanation:

Power is measured in Dioptres (DD). Since it is a convex lens, the focal length and power are positive.

Light Energy (Refraction, Lenses, Dispersion) Revision - Class 8 Science ICSE