Reflection, refraction and lenses

Angle of incidence = angle of reflection.

A real, inverted image is formed.

The wavelength decreases.

Angle of reflection = 35 degrees (1) because the angle of incidence equals the angle of reflection, both measured from the normal (1).

The light slows down as it enters the denser glass (1) and bends towards the normal (1).

magnification = image height / object height = 6 / 2 (1) = 3 (no units) (1).

A real image is formed where light rays actually meet and can be projected onto a screen (1); a virtual image is formed where rays only appear to come from and cannot be projected (1). A magnifying glass produces a magnified virtual image (1).

When the object is beyond the focal point the image is real and inverted (1). Rays from the object are refracted by the lens so they actually converge and meet on the far side (1); because the rays genuinely meet, the image can be projected onto a screen, so it is real (1). If the object is moved closer than the focal length, the rays diverge and the lens produces a magnified, upright, virtual image, as in a magnifying glass (1).

As the ray leaves glass and enters air it speeds up, because air is optically less dense than glass (1); a wave bends away from the normal when it speeds up, so the angle increases from 30 degrees in glass to 48 degrees in air (1); this is consistent with the ray bending away from the normal at the boundary (1)

Total internal reflection occurs when light travelling in a denser medium strikes the boundary with a less dense medium and is completely reflected back into the denser medium, with no transmitted ray (1); the two conditions are: (1) the light must be travelling from a denser medium to a less dense one, and (2) the angle of incidence must be greater than the critical angle for that boundary (1); total internal reflection is used in optical fibres to transmit light (and data) along curved glass cables for internet communications and in medical endoscopes (1)

The object is beyond the focal point, so a real, inverted image is formed on the opposite side of the lens to the object (1); using the lens equation, the image distance is 15 cm from the lens (1); the magnification = image distance / object distance = 15 / 30 = 0.5, so the image is diminished (smaller than the object) (1)

In specular reflection from a smooth mirror, each incident ray obeys the law of reflection and parallel incident rays remain parallel after reflection; rays from a single point on an object all reflect to a corresponding single point in the image, forming a sharp, clear image (1); in diffuse reflection from a rough surface like a wall, the microscopic bumps mean that neighbouring rays strike the surface at many different angles, so they reflect in many different directions (1); scattered rays from a single object point do not converge to a single image point, so no coherent image is formed — you see the wall uniformly bright because it scatters light towards your eyes from every direction (1)

A pulse of light is directed into one end of the optical fibre at a shallow angle so that when it strikes the glass-cladding boundary the angle of incidence is greater than the critical angle; total internal reflection occurs and the light bounces along the fibre without escaping through the sides (1); the glass must have a specific refractive index (and thus critical angle) to ensure that rays travelling along the fibre are always above the critical angle even when the fibre bends; the cladding layer (lower refractive index) ensures the critical angle condition is met (1); advantage: optical fibres can carry much higher data rates than copper cables because light can be modulated at very high frequencies, and signal loss per kilometre is very small (1); limitation: glass fibre is more expensive to manufacture and install than copper cable, and the glass is brittle and can break if bent sharply (1)