Optical Instruments — Formula Sheet

M = 1 + D/f

M = D/f

M = m_o × m_e

m_e = 1 + D/f_e

M = (v_o/u_o) × (1 + D/f_e)

M = (L/f_o) × (1 + D/f_e)

M = f_o / f_e

M = −(f_o/f_e) × (1 + f_e/D)

Length of telescope (normal adjustment) = f_o + f_e

Brightness ratio B = D² / d²

Least Distance of Distinct Vision (D)

The minimum distance (25 cm for a normal eye) at which the eye sees an object clearly without any strain. Represented by D = 25 cm.

The eye is placed close to the lens and the object distance is adjusted until the image appears at the least distance of distinct vision (D = 25 cm).

Angular magnification M = β/α (ratio of angles, not sizes)

Total magnifying power

M = mₒ × mₑ = (vₒ/uₒ) × (1 + D/fₑ)