Ray optics practice · Medium

The correct answer is C (0.041) because the dispersive power is calculated using the focal lengths for red, yellow, and violet rays and the formula $\omega = \frac{{\mu_v - \mu_r}}{{\mu_y - 1}}$.

The correct answer is C (Violet colour) because magnifying power is inversely proportional to the focal length, and violet light has the shortest focal length.

Option B is correct because the blue color of seawater is primarily due to the scattering of sunlight by water molecules, known as Rayleigh scattering.

Option D (Velocity increases) is correct because when light moves from a denser to a rarer medium, its speed increases due to the change in refractive index.

Option B ($45^\circ$) is correct because it is the angle of incidence calculated using the prism formula for minimum deviation.

Option B is correct because the assertion is true (a red object appears dark in yellow light), and the reason is also true (red color is scattered less), but the reason is not the correct explanation.

Option B (is dependent on nature of surface and intensity of light used) is correct because radiation pressure depends on the reflectivity of the surface and the intensity of the incident light.

Option D ($\frac{2}{\sqrt{3}}$) is correct because it accurately calculates the refractive index of the prism using Snell's law.

Option B ($20\,\,cm, - \,30\,\,cm$) is correct because it satisfies the lens combination equations for both the contact and separated lens scenarios.

The correct answer is C ($2 \cos ^{-1}\left(\frac{3}{4}\right)$) because it is the correct prism angle calculated using the refractive index and the angle of minimum deviation.

Option B is correct because the refractive index (μ) of the prism material varies with the wavelength (λ) of light, causing different colors to bend at different angles, leading to the splitting of white light.

Option B (Infinite) is correct because a plane mirror can be considered as a spherical mirror with an infinite radius of curvature, leading to an infinite focal length.

Option A (Shortsightedness) is correct because in shortsightedness, the focal length of the eye lens decreases, increasing its power.

Option A (+50 cm) is correct because a convex lens with a focal length of 50 cm is needed to correct the vision such that objects at 25 cm appear to be at 50 cm.

Option A is correct because a plane mirror creates an upright image when the object is parallel and an inverted image when the object is perpendicular to the mirror.

Option A is correct because the sun's spectrum is a continuous spectrum with dark absorption lines (Fraunhofer lines) caused by elements in the solar atmosphere absorbing specific wavelengths.

Option C ($4\pi$) is correct because the total luminous flux emitted by a 1 candela source is defined as $4\pi$ lumens.

Option A is correct because both the Assertion and Reason are true, and the Reason correctly explains why the critical angle is minimum for violet color due to its higher refractive index.

Option A (0.2 cm) is correct because the distance between the lenses to eliminate spherical aberration is the difference in their focal lengths.

Option C, $\left|\frac{u_1+u_2}{2}\right|$, is correct because it represents the average of the object distances, which corresponds to the focal length when images of the same size are formed.

Option C (9) is correct because the ratio of focal lengths in liquid and air is calculated using the lens maker's formula and refractive indices, resulting in a value closest to 9.

Option A (If both assertion and reason are true and reason is a correct explanation of the assertion) is correct because the shining of a diamond is due to total internal reflection, and the high refractive index of diamond leads to a small critical angle, facilitating total internal reflection.

Option D (Variation in speeds of different colours of light in the prism) is correct because the prism separates sunlight into a spectrum due to different colors having different refractive indices and thus different speeds in the prism.