Making things look bigger or nearer
Optical instruments use convex lenses to form images with a larger angular size than the object gives on its own. This makes small or distant things easier to see.
The magnifying glass
A single convex lens used as a magnifying glass has the object placed inside its focal length. It produces a virtual, upright, magnified image on the same side as the object. A shorter focal length gives greater magnification.
The compound microscope
A compound microscope uses two convex lenses. The objective lens (short focal length) forms a real, inverted, magnified image of a nearby object. The eyepiece lens then acts as a magnifying glass on that first image, giving a very large virtual final image. The total magnification is the product of the two magnifications.
The astronomical telescope
An astronomical telescope also uses two convex lenses. The objective has a long focal length and the eyepiece a short one. In normal adjustment the two lenses are separated by the sum of their focal lengths (f₀ + fₑ).
Key formula / Key formula
Angular magnification of a telescope in normal adjustment: M = f₀ / fₑ
where f₀ = objective focal length, fₑ = eyepiece focal length.
Worked example / Worked example
A telescope has an objective of focal length 100 cm and an eyepiece of focal length 5 cm. Find the magnification and lens separation in normal adjustment.
M = f₀ / fₑ = 100 / 5 = 20 times.
Separation = f₀ + fₑ = 100 + 5 = 105 cm.
Remember / Remember
- Microscope: both lenses short focal length; objective fₒ < eyepiece fₑ.
- Telescope: objective long focal length, eyepiece short; M = f₀ / fₑ.
- The final image in both instruments is virtual and enlarged.