A concave lens has a focal length of 15 cm. If the object is placed at 30 cm from the lens, what is the image distance?

The correct answer is B, it slows down and bends towards the normal. A denser medium has a higher refractive index, and the refractive index is the speed of light in vacuum divided by its speed in the medium, so light must travel more slowly inside it. When the ray meets the surface at an angle, the part of the wavefront that enters first is slowed first, which swings the ray towards the normal. Air to glass and air to water are the standard examples.

Option A takes the correct change of speed with the wrong bending. Option C describes what happens in the opposite case, when light passes from a denser medium to a rarer one. Option D combines two errors at once. A ray that falls along the normal is a special case and passes straight through without bending, though its speed still changes.

The correct answer is C, Isaac Newton. Newton passed a narrow beam of sunlight through a glass prism in a darkened room and obtained a band of seven colours on the wall, which he named the spectrum. He then showed with a second prism that the colours could be recombined into white light, proving that the prism does not colour the light but only separates the colours already present in it. The order of the colours from the base of the prism is remembered as VIBGYOR.

Option A, C. V. Raman, discovered the scattering effect named after him and won the Nobel Prize in 1930. Option B, Lord Rayleigh, explained the scattering that makes the sky blue. Option D, S. Chandrasekhar, worked on the structure and evolution of stars.

The correct answer is B, virtual, erect and of the same size. Rays reflected from a plane mirror diverge and only appear to come from a point behind the mirror, so the image cannot be caught on a screen and is virtual. It stands the same way up as the object, is exactly as large as the object and lies as far behind the mirror as the object is in front of it. It is also laterally inverted, which is why the left hand appears as the right hand and why the word AMBULANCE is painted in reverse on the front of the van so that a driver ahead reads it correctly in the mirror.

Options A and D describe real images, which a plane mirror can never form. Option C describes the image in a convex mirror, which is smaller than the object.

The correct answer is C, a convex mirror. A convex mirror curves outward and spreads the light that falls on it, so it always forms a virtual, erect and diminished image, whatever the distance of the object. Because the image is smaller, a small mirror can show a very wide field of view, and the driver sees a long stretch of the road behind. The same reason puts convex mirrors at blind turnings on hill roads and in shops.

Option A, a plane mirror, would give a true sized image but a narrow field of view. Option B, a concave mirror, converges light and can form a large inverted real image of a distant object, which would be useless and dangerous in a vehicle; it is used instead for shaving, in dentistry and in headlights. Option D is not a mirror of this kind at all.

The correct answer is B, plus 2 dioptres. The power of a lens is the reciprocal of its focal length expressed in metres, that is P equals 1 divided by f. Fifty centimetres is 0.5 metre, and the reciprocal of 0.5 is 2, so the power is two dioptres. The lens is convex and therefore converging, so the power carries a positive sign. Power measures how strongly a lens bends light, so a short focal length means a powerful lens.

Option A takes the focal length in metres as the answer instead of its reciprocal. Option C gives the right number with the wrong sign, which would describe a concave lens. Option D uses the focal length in centimetres in the formula, which is the commonest mistake in this calculation.