Question

You are using a mirror and a camera to make a self portrait. You focus the camera on yourself through the mirror. The mirror is a distance \(\mathrm{D}\) away from you. To what distance should you set the range of focus on the camera? a) \(D\) b) \(2 \mathrm{D}\) c) \(\mathrm{D} / 2\) d) \(4 \mathrm{D}\)

Short answer

Answer: (b) 2D

Step-by-step solution

Visualize the situation

We can visualize this situation as follows. The person is standing in front of the mirror with distance D between them. The camera is focused on the person through the mirror. We need to consider the distance the light travels from the person, to the mirror, and back to the person to find the correct distance to set the camera's focus.

Calculate the total distance between the person and the camera's focus point

We can calculate the total distance that light travels from the person to the mirror and back to the person. Since there is distance D from the person to the mirror, and then an additional D from the mirror back to the person, we have a total distance of 2D. Therefore, the correct distance to set the camera's range of focus is: 2D

Choose the correct answer

Now that we know the correct distance to set the camera's range of focus is 2D, we can choose the correct answer from the options provided: a) D b) 2D c) D / 2 d) 4D The correct answer is option (b) 2D.

Key concepts

Optics

Optics is a branch of physics that encompasses the behavior and properties of light, including its interactions with matter as well as the construction of instruments that use or detect it. When we discuss mirrors in the context of optics, we refer to the phenomenon of reflection, where light bounces off the surface of a mirror. The law of reflection states that the angle at which the light strikes the mirror, known as the incident angle, is equal to the angle at which it reflects away, the reflected angle.

The application of optics is crucial in everyday life, not least in the use of cameras and mirrors for various purposes, including self-portraiture. Understanding reflection is key for manipulating light to our advantage, whether in scientific instruments or in creating the perfect photograph.

Image Formation

Image formation is a central concept in optics where light rays from an object are redirected by an optical device such as a lens or mirror to form an image. There are two types of images – real and virtual. A real image is formed when light rays converge and can be projected onto a screen, while a virtual image, like the one seen in a flat mirror, cannot be projected because the rays only appear to be emanating from a given location behind the mirror.

When you are taking a self-portrait using a mirror, you see a virtual image of yourself. Your camera, however, is designed to focus on real images. So it needs to be set to focus on the point where the light appears to come from - which, through image formation principles, is effectively twice the distance between you and the mirror because the light travels the distance to the mirror and the same distance back.

Range of Focus

The range of focus is an important concept when using any imaging device. It refers to the distance range within which objects are in reasonably sharp focus. Cameras have adjustable focus settings to accommodate how far away the subject is. Setting a camera's focus incorrectly for the subject's distance will result in a blurry image.

In the scenario of taking a self-portrait in a mirror, the range of focus on the camera must be set to the total distance the light travels - from you to the mirror, and back to you. Even though the mirror is only at distance D from you, the light's round trip makes this effectively 2D. Therefore, setting the range of focus to 2D ensures that the virtual image of yourself is in sharp focus for the camera.