Karnataka SSLC 10th Science Question Paper 2024

The relationship between focal length ($f$) and radius of curvature ($R$) for a spherical mirror is $f = \frac{R}{2}$. Given $R = 6$ cm, $f = \frac{6}{2} = 3$ cm. Therefore, the focal length of the convex mirror is 3 cm.

The power ($P$) of a lens is defined as the reciprocal of its focal length ($f$) in meters: $P = \frac{1}{f(\text{in meters})}$. Given $f = 0.2$ m, $P = \frac{1}{0.2} = 5$ D. The power of the convex lens is +5 Dioptre.

Accommodation is the ability of the eye lens to adjust its focal length. The ciliary muscles control the curvature of the lens. To see distant objects, ciliary muscles relax, the lens becomes thin, and focal length increases. To see nearby objects, ciliary muscles contract, the lens becomes thicker (curved), and focal length decreases.

Given: Focal length of concave lens $f = -30$ cm (concave lens focal length is negative). Image distance $v = -20$ cm (concave lens always forms a virtual image on the same side). Using the lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$. Substituting the values: $\frac{1}{-20} - \frac{1}{u} = \frac{1}{-30}$. Rearranging: $-\frac{1}{u} = \frac{1}{20} - \frac{1}{30}$. Taking LCM ($60$): $-\frac{1}{u} = \frac{3-2}{60} = \frac{1}{60}$. Thus, $u = -60$ cm. The object should be placed at a distance of 60 cm from the lens.

Stars twinkle due to atmospheric refraction. Light from the stars enters the Earth's atmosphere and undergoes continuous refraction through various layers of air with varying optical densities (due to temperature and pressure differences). This causes the apparent position of the star to shift slightly and its intensity to fluctuate, which we perceive as twinkling.