Overview: Optical Instruments

The power of changing the focal length of the eye lens to see objects clearly at different distances is called the power of accommodation of the eye.

The far point of a normal eye is the point at infinity, which can be seen distinctly when the eye is in a relaxed state.

The nearest distance up to which the eye can see clearly by applying maximum power of accommodation is called the least distance of distinct vision.

The near point of the eye is the nearest point at which an object can be seen distinctly.

The angle which an object subtends at our eye is called the 'visual angle’.

The magnifying power of an optical instrument is defined as the ratio of the visual angle subtended by the image formed by the instrument at the eye to the visual angle subtended by the object at the unaided eye.

A microscope is an optical instrument which forms a large image of a small and close object so that it subtends a large visual angle at the eye.

A simple microscope is a short-focus convex lens used to obtain a magnified, erect, and virtual image of a close object.

The magnifying power of a simple microscope is the ratio of the angle subtended by the image at the eye to the angle subtended by the object when placed at the least distance of distinct vision.

A compound microscope is an optical instrument which produces high magnification by using two converging lenses: an objective and an eyepiece.

The lens placed near the object, of short focal length and small aperture, is called the objective lens.

The lens placed near the eye, of larger focal length and aperture, is called the eyepiece.

An astronomical telescope is an optical instrument used to observe distant heavenly objects by increasing the visual angle subtended at the eye.

A telescope that uses a concave mirror as the objective to collect and focus light from distant objects.

A reflecting telescope in which a plane mirror inclined at 45° deflects light from a concave primary mirror to an eyepiece placed at the side.

A reflecting telescope that uses a paraboloidal primary mirror with a central hole and a convex secondary mirror, with the eyepiece placed behind the primary mirror.

 The power of an optical instrument to produce distinctly separate images of two close objects is called the ‘resolving power' of that instrument.

Image at least distance of distinct vision:

M = 1 + \[\frac {D}{f}\]

Eye relaxed, image at infinity:

M = \[\frac {D}{f}\]

M = m₀ × m_e

Normal Adjustment, Image at D:

\[{M=\frac{L}{f_o}\left(1+\frac{D}{f_e}\right)}\]

Relaxed Eye, Image at Infinity:

\[{M=\frac{L}{f_o}\frac{D}{f_e}}\]

General Magnifying Power of a Telescope:

M = \[\frac {f_o}{u_e}\]

Final Image at the Least Distance of Distinct Vision:

M = \[\frac{f_o}{f_e}\left(1+\frac{D}{f_e}\right)\]

Normal Adjustment / Final Image at Infinity:

M = -\[\frac {f_o}{f_e}\]

M = -\[\frac {f_o}{f_e}\]

• f_o​ = focal length of the concave (objective) mirror
• f_e​ = focal length of the eyepiece

• A compound microscope uses two convex lenses, an objective (short focal length) and an eyepiece (longer focal length).
• The objective forms a real, inverted, magnified image, which acts as a virtual object for the eyepiece.
• The eyepiece produces a final virtual and highly magnified image, usually at the least distance of distinct vision or at infinity.
• Total magnifying power is the product of the magnifications of the objective and the eyepiece.
• Large magnification is achieved when the object is placed close to the objective's focal point and the eyepiece has a short focal length.

• For relaxed eye adjustment, the final image is formed at infinity, and the intermediate image lies at the focus of the eyepiece.
• Magnifying power (relaxed eye) is
  M = \[\frac {L}{f_o}\]\[\frac {D}{f_e}\].
• Maximum magnification is obtained when the object is placed very close to the focal point of the objective.
• A bright, highly magnified image requires lenses with short focal lengths, with the objective having a small aperture.
• A compound microscope is used instead of a simple microscope to achieve higher magnification without sacrificing image quality.

• An astronomical refracting telescope uses two convex lenses—an objective near the object and an eyepiece near the eye.
• The objective lens has a large focal length and a large aperture, so it can collect more light from distant objects.
• The objective forms a real, inverted, and diminished image of the distant object at its focal plane.
• This image serves as an object for the eyepiece, producing a magnified virtual image for the observer.
• Normal adjustment is done by making the final image at infinity, so the eye observes without strain.
• Refracting telescopes suffer from chromatic and spherical aberrations and have limited magnification and resolution.

• According to Rayleigh’s criterion, two-point objects are just resolved when the principal maximum of one diffraction pattern falls on the first minimum of the other.
• Resolving power increases when the limit of resolution decreases; smaller separation means better resolution.
• For a telescope, the limit of resolution depends on wavelength and aperture, and a larger aperture gives higher resolving power.
• For a microscope, resolving power improves with a smaller wavelength of light and a larger numerical aperture.
• Electron microscopes have very high resolving power because electrons have extremely small wavelengths compared to visible light.