9.7.1. The microscope

A simple magnifier or microscope is a converging lens of small focal length (Fig. 9.23). In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side.

A simple microscope uses a converging lens with a small focal length. When using it, the lens is placed very close to the object, ideally at a distance equal to its focal length or less. This arrangement allows the lens to create a magnified image that can be viewed comfortably by the eye. When the eye is close to the lens, it can focus easily on the image produced by the lens, resulting in magnification of the small object.

Think of looking through a magnifying glass to read the fine print on a label. By bringing the magnifying glass close to the text, you're effectively using a simple microscope that allows your eye to see the letters much larger than they appear to the naked eye.

The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i.e., at 25 cm or more.

The microscope is designed to produce an erect (upright), magnified, and virtual image, which is perceived by the eye as being closer than its actual position. The optimal viewing distance for comfortable observation is generally around 25 cm. A virtual image is one that cannot be projected onto a screen because the light rays appear to diverge from the image location rather than converging at that point.

Imagine holding a smartphone's camera to take a picture of a small flower petal. As you bring your camera lens close to the petal, you see a detailed, enlarged image on the screen. Even though the image looks large, it is virtual, and the phone's screen cannot capture a physical representation of the flower—it is a mere reflection of the light coming from the petal.

Although the closest comfortable distance for viewing the image is when it is at the near point (distance D ≈ 25 cm), it causes some strain on the eye.

While images viewed through microscopes can be comfortably focused at around 25 cm, this distance can cause eye strain if maintained for prolonged periods. Therefore, adjusting the lens or distance can help reduce this strain and allow for clearer viewing.

When using a pair of binoculars to focus on a bird in the distance, you might feel comfortable at a certain distance, but if you keep adjusting your focus too closely, it can lead to fatigue in your eyes. Similarly, when using a microscope, keeping the image at a distance that accommodates your vision is essential to avoid discomfort.

If the object is at a distance f, the image is at infinity. However, if the object is at a distance slightly less than the focal length of the lens, the image is virtual and closer than infinity.

When the object is placed exactly at the focal length (f), the light rays focus to form the image at a point far away, effectively at infinity. On the other hand, if the object is closer than the focal length, it results in a virtual image that remains within reach, making it observable without the need for advanced optics to capture it.

Think of a camera lens set to capture the sunset. If you set the focus to a point in the distance (at infinity), the sunset is perfectly clear. But if you point the camera at the trees close by without adjusting the focus, you'll see nothing but a blurry image, akin to observing a virtual image that is not sharp but is ever so enticing.

The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation m = D/f.

In a simple microscope, the linear magnification is calculated using the formula m = D/f, where D is the near point distance (about 25 cm) and f is the focal length of the lens. This means that the magnification increases as the focal length decreases, allowing for stronger magnification capabilities with shorter focal lengths.

When looking closely at a small insect through a magnifying glass, if you adjust the lens to a shorter focal length, you can see almost every detail of the insect, such as the texture of its wings. This adjustment gives you not just a better view but also a more substantial apparent increase in size, just like adjusting the settings on your camera to capture finer details.

We will now find the magnification when the image is at infinity. In this case we will obtain the angular magnification.

When the image is formed at infinity, we calculate the angular magnification by comparing the angles subtended by the object and the image at the eye. This is important for understanding how much the image can be enlarged based on the setup and position of the lenses used. The formula helps distinguish between simple linear magnification and the more practical angular magnification that affects real-world viewing experiences.

Think about viewing distant mountains through a telescope. As you look, the mountains seem to fill up more of your field of vision, giving you an immersive experience of their massive peaks. This is similar to how angular magnification allows you to perceive small objects much larger than they are by simply manipulating light and angles through lenses.

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