Light and the Eye
Reflection and refraction of light
Apply the New Cartesian Sign Convention to the mirror and lens formulae, work out magnification and the power of a lens, and read a refractive index for what it says about the speed of light.
A pencil standing in a glass of water looks broken at the surface. A coin that has just vanished below the rim of a bowl comes back into view when someone pours water in. Neither the pencil nor the coin has moved. Light travelling obliquely from one transparent medium into another changes direction — refraction — and how much it changes tells you something exact about the two media.
Signs before arithmetic
The mirror formula is 1/v + 1/u = 1/f and the lens formula is 1/v − 1/u = 1/f. Neither is any use until the signs are right. Measure everything from the pole of the mirror, or the optical centre of the lens, along the principal axis. The object goes on the left, so its distance is negative. Distances to the right of the origin count positive, distances to the left negative. A convex lens has a positive focal length, a concave lens a negative one.
Worked example
A magnification comes out as −2. What does that tell you about the image, before you know anything else?
The number 2 says the image is twice the height of the object.
Magnification is the height of the image over the height of the object, so its size is the whole of what the magnitude reports.
Try it together
An object stands 30 cm in front of a concave mirror whose focal length is 15 cm.
Work in the New Cartesian Sign Convention, and answer with a bare number each time, sign included.
1.The object is on the left of the mirror, so its distance is measured along the negative direction. What is the object distance u?
Have a go
Have a go on your own. A convex mirror has f = +15 and an object sits at u = -30. Use 1/v = 1/f − 1/u to find v. Answer with a number, sign included.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.