Question

Please show all work and formulas!

4. A strong microscope objective lens "100

Answer 1

Lens Maker's Formula

It is a relation that connects focal length of a lens to radii of curvature of the two surfaces of the lens and refractive index of the material of the lens.

The following assumptions are made for the derivation:

• The lens is thin, so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centre of the lens.

• The aperture of the lens is small.

• Point object is considered.

• Incident and refracted rays make small angles.

<img align="middle" data-cke-saved-src="http://images.tutorvista.com/content/optics/lens-maker-s-formula-concex-lens.gif" src="http://images.tutorvista.com/content/optics/lens-maker-s-formula-concex-lens.gif" width="451" height="278" title="ray diagram for lens maker s formula using concex lens" "="" style="border: 0px;">

Consider a convex lens (or concave lens) of absolute refractive index m₂ to be placed in a rarer medium of absolute refractive index m₁.

Considering the refraction of a point object on the surface XP₁Y, the image is formed at I₁ who is at a distance of V₁.

CI₁= P₁I₁ = V₁ (as the lens is thin)

CC₁ = P₁C₁ = R₁

CO = P₁O = u

It follows from the refraction due to convex spherical surface XP₁Y

The refracted ray from A suffers a second refraction on the surface XP₂Y and emerges along BI. Therefore I is the final real image of O.

Here the object distance is

(Note P₁P₂ is very small)

(Final image distance)

Let R₂ be radius of curvature of second surface of the lens.

\ It follows from refraction due to concave spherical surface from denser to rarer medium that

Adding (1) & (2)

Spatial Resolution

A telescope's spatial (or angular) resolution refers to how well it can distinguish between two objects in space which are separated by a small angular distance - it is the telescopes ability to resolve fine detail. The closer two objects can be while still seen as two separate objects, the higher the spatial resolution of the telescope. The spatial resolution of a telescope affects how well details can be seen in an image. A telescope with higher spatial resolution creates clearer and more detailed images. As an analogy, lets think of our eyes as being visible light detectors. A person's eyes have high spatial resolution if, for example, they can see the letters on a page as being sharp, clear and distinct.

A lower (left) and higher (right) resolution image of the Andromeda galaxy

The spatial resolution of a telescope depends on the size of its lenses or mirrors and the size of the pixels in its detectors. The resolution is also limited by air turbulence (for ground based observatories) and by the smoothness of a telescope's mirrors or lenses. The spatial resolution of a telescope is proportional to the wavelength of light being detected divided by the diameter of the telescope. Larger telescopes have better spatial resolution. However, it is the size of the telescope relative to the wavelength that really counts. The longer the wavelength, the larger the telescope needs to be to get good resolution.

Spatial resolution is usually measured in units of arcseconds or arcminutes. Our eyes, for example have a spatial resolution of about one arcminute.

The Spitzer Space Telescope will provide unprecedented resolution in the infrared region of the electromagnetic spectrum. The simulated images below, show the improvement in the spatial resolution of Spitzer (right) when compared with two previous infrared space missions: IRAS (left - launched in 1983) and ISO (center - launched in 1995).

IRAS (left), ISO (center) and Spitzer (right) simulated view of the same region of space

Definition of terms

Resolving power is the ability of an imaging device to separate (i.e., to see as distinct) points of an object that are located at a small angular distance. The term resolution or minimum resolvable distance is the minimum distance between distinguishable objects in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power. In scientific analysis, in general, the term "resolution" is used to describe the precision with which any instrument measures and records (in an image or spectrum) any variable in the specimen or sample under study.

Explanation

Airy diffraction pattern generated by a plane wave falling on a circular aperture, such as the pupil of the eye

The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality