7.2 Optical Instruments

The function of an optical instrument is related to the type of image—real or virtual—and the size of the image formed by its lenses.
Image size depends on the object’s position from the centre of the lens.
Examples include a magnifying glass, microscope, astronomical telescope, camera, smartphone, LCD projector, spectacles and closed-circuit television (CCTV).

Formation of the Final Image by a Microscope

A microscope uses two convex lenses: the objective lens and the eyepiece.

Place the object between $F_{o}$ and $2 F_{o}$ of the objective lens.
The objective lens forms the first image, $I_{o}$ , farther than $2 F_{o}$ .
The first image is real, inverted and magnified and acts as the object for the eyepiece.
The first image lies between $F_{e}$ and the optical centre, $O$ , of the eyepiece.
The eyepiece acts as a magnifying glass and forms a virtual, upright and magnified image relative to the first image.
The final image, $I$ , is virtual, inverted and magnified relative to the original object.

Symbols:

$F_{o}$ : focal point of the objective lens
$F_{e}$ : focal point of the eyepiece
$I_{o}$ : first image formed by the objective lens
$I$ : final virtual image

Magnifying Power of a Microscope

Magnifying power of microscope = magnifying power of objective lens \times magnifying power of eyepiece

Example: Objective lens $= 40 \times$ ; eyepiece $= 4 \times$ .

Magnifying power = 40 \times 4 = 160 times

Select objective lenses and eyepieces with suitable magnifying powers for observing tiny objects of different sizes.

Formation of the Final Image by a Telescope

A simple astronomical telescope uses two convex lenses: the objective lens and the eyepiece.

Parallel incident rays from a distant object enter the objective lens.
The object is effectively at infinity; the objective lens forms the first image, $I_{o}$ , at $F_{o}$ .
The first image is real, inverted and diminished.
The first image is positioned at $F_{e}$ of the eyepiece and acts as the object for it.
The eyepiece forms a virtual, upright and magnified image relative to the first image.
The final image, $I$ , is at infinity and is virtual, inverted and magnified relative to the distant object.

Normal Adjustment and a Simple Telescope

For comfortable viewing under normal adjustment:

distance between objective lens and eyepiece = f_{o} + f_{e}

where:

$f_{o}$ = focal length of the objective lens;
$f_{e}$ = focal length of the eyepiece.

Activity 7.3 — Aim: Build a simple telescope model.

Materials: Hollow paper cylinder and cellophane tape
Apparatus: Convex lens with $f_{o} \geq 10 cm$ , convex lens with $f_{e} \leq 2 cm$ , ruler, scissors or knife, and pencil

Identify the type, size and function of each telescope lens.
Select the objective lens and eyepiece needed to produce the clearest and brightest image.
Use the ray diagram for image formation in a simple telescope as the design guide.
Sketch the telescope, placing the objective lens and eyepiece at opposite ends of an opaque hollow cylinder.
Build the model according to the sketch.
Adjust the separation of the lenses to $f_{o} + f_{e}$ for normal adjustment.
Evaluate the design’s effectiveness and improve it.

The cylinder must be opaque to prevent unwanted light from entering and interfering with the image.
In normal adjustment, the objective lens and eyepiece are separated by $f_{o} + f_{e}$ .

Applications of Lenses in Optical Instruments

Optical instrument	Application of lenses
Camera / smartphone	Forms images for photographs and videos; different camera lenses provide different fields of vision.
LCD projector	Forms a projected image for viewing on a screen.
Spectacles	Help overcome limitations of human sight.
Magnifying glass	Produces a virtual, upright and magnified image when $u$ < $f$ . A water lens can also function as a magnifying glass.
CCTV / spy camera	Uses small lenses to form images for monitoring and safety devices.

Advances in optics allow lenses in smartphones and CCTV systems to be only several millimetres thick.
Flat lenses can be only several microns thick, where $1 micron = 0.001 mm$ .
In a DSLR camera, focal length affects the field of vision:
- shorter focal length $\to$ wider field of vision;
- longer focal length $\to$ narrower field of vision.
For photographs taken from the same distance, a $24 mm$ lens gives a wider field of vision than a $70 mm$ lens.
Science and technology contribute to optical instruments that help overcome limitations of human sight.