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 \(D\) away from you. To what distance should you set the range of focus on the camera? a) \(D\) b) \(2 D\) c) \(D / 2\) d) \(4 D\)

Short answer

Answer: (b) 2D

Step-by-step solution

Set up the problem

You are standing a distance \(D\) away from the mirror, with the camera focused on your image through the mirror. The distance between you and the camera should be the same as the distance between the camera and your image in the mirror.

Calculate the distance between the camera and the image in the mirror

Since the camera is focused on your image through the mirror, the distance it sees is the sum of the distances from you to the mirror, and from the mirror to your image. These two distances are equal because it is a reflection, so the total distance is \(D + D = 2D\).

Set the range of focus on the camera

Now we know the total distance the camera needs to focus on is \(2D\). Therefore, you should set the range of focus on the camera to \(2D\). The correct answer is (b) \(2D\).

Key concepts

Optical Physics

Optical physics is a study of light and its interaction with matter. Understanding the principles of how light behaves is fundamental to various applications, including photography, which is the essence of our exercise.

When we discuss mirrors and cameras, we're dealing with visible light's journey from one point to another and its reflection—light bounces off the mirror to create an image. The light's path follows well-defined principles, such as the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

This principle is crucial when considering the distance between a camera, a mirror, and the object being reflected. In our case, the exercise requires us to find the correct focus setting by understanding how far the light travels from the person to the camera via the mirror. This involves the inherent properties of light and the laws that govern its reflection.

Geometric Optics

Geometric optics is the aspect of optical physics that deals with the approximation in which light travels in straight lines. This is the perfect framework for high school physics problems involving lenses and mirrors, as in our example.

Mirrors, specifically flat or plane mirrors, reflect light such that the angle of incidence equals the angle of reflection. Moreover, images formed by plane mirrors are virtual, meaning they cannot be projected onto a screen since light does not actually come from the image's apparent position behind the mirror.

In our self-portrait example, the camera's focus must be set based on these virtual images. The virtual image of oneself seen in the mirror is behind the mirror at the same distance as the actual distance to the mirror. Thus, when we sum these distances together, it tells us how far the camera perceives the image to be.

Lens and Mirror Calculations

Lens and mirror calculations involve using mathematical equations to determine properties like focal length, image distance, and object distance. These calculations are a staple in optics and vital for photographers, scientists, and optometrists, to name a few.

In the context of our mirror reflection challenge, the equation to use is not complex because we are dealing with a flat mirror. The distance from the observer to the mirror equals the distance from the mirror to the image. As we concluded in the steps, since both distances are equal to D, the camera must focus on an image twice as far away as the distance to the mirror. Therefore, the camera should focus at a distance of 2D.

The simplicity of the flat mirror calculations in geometric optics is beautiful yet powerful, allowing us to accurately set the range of focus. Remember, this straightforward additive rule only applies to plane mirrors, and calculations for curved mirrors or lenses involve more intricate formulas and concepts.