Optical systems: thin lenses and mirrors

In the optics kit in the laboratory there are two lenses: one is thicker at the centre than at the edges, and the other is thicker at the edges than at the centre.

1. a) State which one is converging and which one is diverging.
2. b) Describe what happens to a beam of rays parallel to the optical axis when passing through each of them: do they converge at a point or diverge as if coming from a point?

An object is placed in front of a converging lens at a distance greater than twice its focal length.

1. a) State the rules for drawing the three principal rays of a converging lens (the ray parallel to the axis, the ray passing through the centre, and the ray passing through the object focus).
2. b) Draw the ray diagram in your notebook and determine the characteristics of the image: is it real or virtual, upright or inverted, larger or smaller than the object?

You can do it on paper and send a photo with your answer.

A watchmaker uses a magnifying glass to inspect the mechanism of a watch.

1. a) What type of lens is a magnifying glass: converging or diverging?
2. b) Where must the object be placed relative to the focus of the lens for the magnifying glass to work?
3. c) State the characteristics of the observed image (real or virtual, upright or inverted, larger or smaller).

A luminous object is placed $s = 30\ \text{cm}$ from a thin converging lens with focal length $f = 10\ \text{cm}$. Use the thin lens equation $1/f = 1/s + 1/s'$ with this sign convention: $s$ is positive for a real object, $s'$ is positive if the image is real and negative if virtual, and $f$ is positive for converging lenses and negative for diverging lenses.

1. a) Calculate the image distance $s'$.
2. b) State whether the image is real or virtual and whether it can be projected onto a screen.

A magnifying glass is a converging lens of focal length $f = 10\ \text{cm}$. A stamp placed $s = 6\ \text{cm}$ from the lens is observed. Observe the diagram:

1. a) Calculate the image distance $s'$ and explain the meaning of its sign.
2. b) Calculate the magnification and explain the meaning of its sign.
3. c) State the characteristics of the image and why it cannot be formed on a screen.

The wing mirror of a car is a convex mirror with focal length $f = -0,5\ \text{m}$. A car $1,5\ \text{m}$ high is travelling $s = 10\ \text{m}$ from the mirror. Observe the diagram:

1. a) Calculate the position of the image.
2. b) Calculate the magnification and height of the image.
3. c) In light of the result, explain the meaning of the warning "objects in mirror are closer than they appear".

An object $10\ \text{cm}$ high is placed $s = 60\ \text{cm}$ from a converging lens with focal length $f = 20\ \text{cm}$. Use $1/f = 1/s + 1/s'$ and the magnification $A = -s'/s$, with the usual sign convention (positive distances for real objects and real images). Observe the diagram:

1. a) Calculate the image distance $s'$.
2. b) Calculate the magnification and the height of the image.
3. c) Describe the image: real or virtual, upright or inverted, larger or smaller.

A concave spherical laboratory mirror has a radius of curvature of $R = 40\ \text{cm}$. An object $4\ \text{cm}$ high is placed $s = 30\ \text{cm}$ from the mirror. Recall that $f = R/2$ and use the same equation $1/f = 1/s + 1/s'$ with the usual convention (positive distances for real objects and images). Observe the diagram:

1. a) Calculate the focal length of the mirror.
2. b) Calculate the position of the image.
3. c) Calculate the magnification and height of the image, and state whether it can be captured on a screen.

It is desired to design a projector that forms a real image three times larger than the object on a screen located $4\ \text{m}$ from the object. Observe the diagram:

1. a) Given that for a real image the object-screen distance is $s + s'$, set up the system of equations with the magnification condition $|A| = s'/s = 3$ and calculate $s$ and $s'$.
2. b) Calculate the focal length of the required lens and its power in dioptres.
3. c) Reason why a diverging lens would not be suitable for this project.

Match each application with the type of mirror and briefly explain why: a car's wing mirror, a dentist's mirror used to view a magnified tooth, and a car headlight mirror directing light from the bulb forward in an almost parallel beam.

1. a) Wing mirror.
2. b) Dentist's mirror.
3. c) Headlight mirror.

During an eye test, a hypermetropic (long-sighted) patient is prescribed lenses of $+2\ \text{D}$ and a myopic (short-sighted) patient is prescribed lenses of $-2,5\ \text{D}$. Recall that $P = 1/f$ with $f$ in metres.

1. a) Calculate the focal length of each lens and state its type.
2. b) Explain what focusing problem each patient has (where is the image of a distant object formed relative to the retina?) and why the sign of their lens corrects it.

A refracting telescope belonging to an astronomy club has an objective lens of focal length $f_{\text{ob}} = 90\ \text{cm}$ and an eyepiece of $f_{\text{oc}} = 3\ \text{cm}$. For a very distant object, the angular magnification of the telescope is $M = f_{\text{ob}}/f_{\text{oc}}$ and the length of the tube is approximately the sum of the two focal lengths. Observe the diagram:

1. a) Calculate the angular magnification of the telescope.
2. b) Calculate the approximate length of the tube.
3. c) Explain the role of each lens and why it is desirable for the objective to have a large diameter (think about the light it captures from a faint star).