Intensity and refractionEdexcel International A Level Physics: Revision notes

The intensity of radiation is the power incident on a surface per unit area, I = P/A, in W m⁻². P is the power (energy per second) arriving at right angles to the surface of area A.

For a point source radiating uniformly in all directions, the power is spread over a sphere of area 4πr², so I = P/4πr². Intensity is therefore inversely proportional to the square of the distance: doubling the distance cuts the intensity to a quarter.

Worked example. A 40 W lamp: at r = 2.0 m, I = 40 / (4π × 2.0²) = 0.80 W m⁻².

Light changes speed when it passes from one medium to another. The refractive index of a medium is n = c/v, where c is the speed of light in a vacuum (3.00 × 10⁸ m s⁻¹) and v is the speed of light in the medium. Because v is always smaller than c, n is always greater than 1.

For example, glass with n = 1.50 has v = 3.00 × 10⁸ / 1.50 = 2.00 × 10⁸ m s⁻¹. The refractive index of air is taken as 1.

Refraction is the change in direction of a wave when its speed changes at an interface. At the boundary between media 1 and 2, n₁ sin θ₁ = n₂ sin θ₂, with the angles measured from the normal.

When light enters a medium of higher refractive index it slows down and bends towards the normal; when it enters one of lower index it bends away from the normal. A ray along the normal is not deviated.

Worked example. Air to glass (n = 1.50), θ₁ = 40°: sin θ₂ = sin 40° / 1.50 = 0.429, so θ₂ = 25°.

When light passes through a block with parallel faces, the angle of refraction at the first face equals the angle of incidence at the second face. Applying n₁ sin θ₁ = n₂ sin θ₂ at both faces shows that the emergent ray is parallel to the incident ray, but displaced sideways.

For air (n = 1) into glass and back, sin θ = n sin θ_g at the second face gives back the original angle.

Place a rectangular block on paper and draw round it. Send a narrow ray from a ray box into one face, mark the incident and emergent rays, then remove the block and join the marks to find the ray inside. Measure the angles of incidence i and refraction r from the normal with a protractor.

Repeat for a range of angles. Since sin i = n sin r for a ray from air, a graph of sin i against sin r is a straight line through the origin with gradient n. Using the gradient of the line of best fit reduces the effect of random errors in individual readings.