Index correction for object = $-0.2$ → $u_{corr} = -30 + (-0.2) = -30.2$ cm
(Correction increases actual object distance by 0.2 cm)
Index correction for image = $-0.3$ → $v_{corr} = 60 + (-0.3) = 59.7$ cm
Answer: -30.2 cm and 59.7 cm
Simple microscope: angular magnification $m = 1 + D/f$ (D=25 cm). Compound microscope: $m = m_o \times m_e = \frac{L}{f_o}(1+D/f_e)$ where $L$ = tube length. Telescope (astronomical): $m = f_o/f_e$; large $f_o$ (objective) needed for distant objects. Telescope for terrestrial use: erecting lens added (or Galilean type with diverging eyepiece) to give erect image.
Spherical aberration: marginal rays focus at different point than paraxial rays (both chromatic and monochromatic). Corrected using: smaller aperture (reduce marginal rays), plano-convex lens properly oriented. Chromatic aberration: different wavelengths focus at different points (because $n$ depends on $\lambda$). Corrected using: achromatic doublet (crown glass + flint glass). Astigmatism, coma, distortion: other lens defects.
Normal eye: far point = infinity (can see objects at any distance). Near point = 25 cm (least distance of distinct vision, D). Myopia (short-sightedness): far point < infinity → concave lens correction. Hypermetropia (long-sightedness): near point > 25 cm → convex lens correction. Presbyopia: loss of accommodation with age (near point increases) → bifocal or reading glasses. Astigmatism: cornea not spherical → cylindrical lens correction.
Young\'s double slit experiment: $y_n = n\lambda D/d$ (bright fringe), $(2n+1)\lambda D/2d$ (dark fringe). Fringe width $\beta = \lambda D/d$. Conditions: fringe width increases with $\lambda$ (larger for red than violet), with $D$ (screen distance), decreases with $d$ (slit separation). Coherent sources required (same frequency, constant phase difference). Single slit diffraction: central maximum width $= 2\lambda/a$ (angular). Polarisation: Malus\'s law: $I = I_0\cos^2\theta$. Brewster\'s angle: $\tan\theta_B = n$ (for complete polarisation of reflected light).