Try these "busters" to exercise your brain ... they should help you grasp the concepts underlying mirrors, lenses, etc. To gain the maximum effect you should attempt to answer them before looking at the answers!
[1] Convex mirrors are often used as rear-view mirrors on cars and trucks to give a wide-angle view. Often, at the bottom of the mirror you see the following ... "Warning, objects are closer than they appear." Yet, according to a ray diagram, the image distance for distant objects is much smaller than the object distance. Why, then, do they appear more distant?
[2] Can the image formed by a concave mirror ever be projected directly onto a screen without using other mirrors or lenses? What about a convex mirror?
[3] In class, we have concentrated on the properties of spherical concave or convex mirrors. We defined the focal point as the point where rays originally traveling parallel to the optical axis, cross, after being reflected, as shown below in (a).
However, simple geometry shows that rays that are distant from the principal axis miss the focal point, as shown in (b). Can this problem be overcome? If so, how?
[4] When you look at yourself reflected in the reverse side of a shiny spoon held at arm's length you see yourself upright. Yet, when you look at yourself reflected in the other side of the spoon you see yourself upside down. Can you explain what's goping on?
[5] Plane mirrors and convex mirrors both form virtual images. With a plane mirror, the distance of the image behind the mirror is unlimited; it is the same as the object distance. So, in principle, the maximum image distance is infinite. For an object in front of a convex mirror, what is the greatest distance behind the mirror an image can form?
[6] Imagine that a spherical mirror and a lens are immersed in water. Compared with the way they operate in air, which one is more affected by the presence of the water? Why?
[7] To an underwater swimmer without goggles, objects appeared blurred and out of focus. However, when the swimmer wears goggles that keep water away from their eyes, objects appear sharp and in focus. How do goggles improve vision underwater?
[8] According to the lens maker's formula, viz:
the focal length, f, of a lens depends on the refractive indices, n1 and n2, of the first and second media. Imagine a glass lens in air ... in class we found that the refractive index of glass depends on the wavelength of the light used. Does this mean that for all lenses, red light and blue light have different focal points? Is this likely to cause problems?
[9] If you send a parallel beam of light through a convex glass lens immersed in water in an aquarium is the focal point closer to or farther away from the lens than the focal point in air?
[10] Here's a good one! A lens is used to image an object on a screen. What happens if half the lens is covered up? Do you see only half the image or what?
[11] The lens is an overhead projector forms an image P' of a point P on an overhead transparency.
If the screen is moved farther way from the projector, should you move the lens up, or down, or simply leave it where is was, in order to keep the image in focus? Explain your reasoning.
[12] (Great question this!) Can you figure out what happens to a parallel beam of light that falls on a lens that is located in a more dense medium, i.e., a medium with a higher refractive index than the lens material?
For example, it could be a lens-shaped "bubble" of air in a block of glass.
[13] An often ignored scenario! In class, we normally only deal with constructing the images of simple, one-dimensional objects. But what happens in the case of two-dimensional objects? What shape and size are the images of the rectangular object in the concave mirror, at the three different object positions shown below? For example, are they rectangular in shape? ... where are they positioned?
[14] Similar to question [13], can you figure out what is the shape, size and position of the image of the rectangular object in the convex mirror, shown below?
[15] (Be careful!) It's nightime and you are looking at the reflection of the Moon in a puddle of water. Question ... how far away from you is the image?