Microscopes

Seeing small objects

A microscope helps the eye see objects too small to resolve clearly unaided. It does this by increasing the angular size of the image and by collecting light in a controlled way. Magnification is useful, but resolution is equally important. A blurry enlarged image does not reveal more detail.

Simple magnifier

A simple magnifier is a single converging lens used with the object inside the focal length. It forms a virtual, upright, enlarged image. The eye views this image as though it were farther away and larger in angular size.

For a relaxed eye viewing the image at infinity, the angular magnification is approximately

M=rac{25 cm}{f}

where $f$ is the lens focal length and $25 cm$ is the conventional near-point distance.

Compound microscope

A compound microscope uses two main lens systems: the objective and the eyepiece. The objective lens is close to the object and has a short focal length. It forms a real, enlarged intermediate image. The eyepiece then acts like a magnifier, producing a final virtual image for the eye.

The total magnification is approximately

$M_{total}=M_{objective}M_{eyepiece}$

For a tube length $L$, objective focal length $f_o$, and eyepiece focal length $f_e$, a simplified estimate is

ight)left(rac{25 cm}{f_e} ight)$$ ## Resolution limit Magnification alone cannot overcome diffraction. The smallest resolvable distance in a microscope is limited approximately by $$dapprox rac{0.61lambda}{NA}$$ where $lambda$ is wavelength and $NA$ is numerical aperture. Numerical aperture is $$NA=nsin heta$$ where $n$ is the refractive index of the medium between specimen and objective, and $ heta$ is the half-angle of collected light. ## Why oil immersion helps Oil immersion objectives use oil with refractive index greater than air between the specimen and lens. This increases $n$, increasing $NA$, and improving resolution. It also reduces refraction losses at glass-air boundaries. This is why high-resolution light microscopy often uses immersion oil. ## Brightness and contrast Small transparent specimens may not absorb much light, so contrast can be low. Techniques such as staining, dark-field microscopy, phase contrast, differential interference contrast, and fluorescence microscopy improve visibility by converting small optical differences into brightness or color differences. Wave optics is essential for understanding many of these techniques. ## Depth of field Microscopes have shallow depth of field, especially at high numerical aperture. Only a thin layer of the specimen is sharply focused at once. This can be useful for optical sectioning but requires careful focusing. ## Beyond visible light Resolution improves with shorter wavelength. Electron microscopes use electron wave behavior with much shorter effective wavelengths than visible light, allowing much higher resolution. However, they require different physics, vacuum systems, and sample preparation. ## The big idea Microscopes use objective and eyepiece optics to increase angular size, but their useful detail is limited by diffraction and numerical aperture. Good microscopy balances magnification, resolution, contrast, brightness, and sample preparation.