Question

The image of yourself that you see in a bathroom mirror is a) left-right inverted. b) front-to-back inverted. c) bottom-to-top inverted. d) not inverted.

Short answer

Answer: a) left-right inverted.

Step-by-step solution

Understand the properties of plane mirrors.

A plane mirror forms a virtual and erect image of the object, which is the same size as the object and is situated at the same distance behind the mirror as the object is in front of the mirror. The object and image are symmetrical concerning the mirror.

Analyze the image in a plane mirror.

When we look at ourselves in the mirror, we see an image that appears to be reversed. The effect is that anything on our right appears on the left of the image and vice versa. This is due to the symmetrical properties of the plane mirror: when we extend our left hand towards the mirror, the image's right hand comes closer. However, the top-to-bottom orientation remains unchanged as the image formed in the mirror is erect.

Determine the orientation of the image.

Based on the properties of plane mirrors and the analysis of the image, we can conclude that the orientation of the image in a bathroom mirror is left-right inverted. This corresponds with option (a). So, the final answer is: a) left-right inverted.

Key concepts

Virtual and Erect Image

When encountering plane mirrors, such as the one in your bathroom, the image you see might seem just as tangible as the real object, but it's actually a virtual image. Unlike a real image, which can be projected onto a screen, a virtual image can't be caught on a surface because its light rays diverge; the mirror just appears to be gathering them from a point behind it.

Now, think about how you stand upright in front of that bathroom mirror: your reflection is also upright, isn't it? This is what we mean when we say the image is erect. It simply means that the image maintains the same vertical orientation as the actual object. For instance, if you raise your arm above your head, the image's arm also goes up, not down. So, keeping in mind our mirror guidelines, the next time you see your virtual reflection standing erect in the mirror, you'll know it's not just 'magic', but physics at play.

Symmetry in Plane Mirrors

A plane mirror, like the one you use daily, creates a fascinating effect of symmetry. Have you ever noticed that your reflection is a mirror image of yourself? It's a bit like standing face-to-face with your twin, except you can't actually shake hands. The reason behind this phenomenon is the symmetrical nature of reflection.

The reflected rays from a plane mirror make it seem as if each point on your body has a corresponding point on your image, tied together invisibly at the mirror's surface. If you draw an imaginary line from a point on your nose straight to the mirror and beyond, you'd find the nose of your reflection at the other end. This line we just pictured is called the 'line of symmetry' or 'axis of reflection.' It illustrates how every point is reflected directly across the mirror to a corresponding opposite location in the virtual image.

Image Inversion

One particularly intriguing aspect of reflections in plane mirrors is image inversion. This is the flipping effect that you witness when looking at yourself in the mirror. However, it's not a complete inversion. Your head does not appear where your feet are, right? Instead, what you experience is a left-right inversion.

This form of inversion is where the left side of the object (that's you waving in the mirror!) appears on the right side of the image, and vice versa. This lateral inversion is because the mirror flips the image along the vertical plane - think of it as reversing the x-axis on a graph. Now, why doesn't this happen top-to-bottom? Because your vertical axis isn't reversed! If you apply some face paint on your forehead, your reflection also sports it at the top, just as expected. It's essentially the reason why if you wear a shirt that reads 'AMBULANCE' in the mirror, it looks backward but still right-side up.