Ray optics practice · Mixed difficulty

Option C (A convex mirror) is correct because convex mirrors always produce diminished, virtual, and erect images.

Option D (1.5) is correct because it is the correct refractive index calculated from the given focal lengths when the lens is silvered on different sides.

Option A (To increase the intensity of image) is correct because a larger aperture allows more light to pass through, increasing the image's intensity.

The correct answer is A (Close to the lens) because the magnification of a simple microscope is maximum when the eye is placed close to the lens.

Answer A (3) is correct because the ratio $F_1/F_2$ is calculated using the given condition $\tan \theta = 2\mu$ and the formulas for $F_1$ and $F_2$.

Option D (Between F and optical centre) is correct because a convex lens produces a positive magnification (virtual and erect image) only when the object is placed between the focus and the optical center.

Option D (None of these) is correct because the speed of light in a vacuum is a fundamental constant, independent of frequency, wavelength, or the source's velocity.

Option B (High refractive index) is correct because the high refractive index leads to a small critical angle and total internal reflection.

Option A (${\sin ^{ - 1}}\,\,\left( {\frac{5}{6}} \right)$) is correct because it is the critical angle calculated using Snell's law and the given speeds of light in the two media.

Option A is correct because a hollow prism with the same refractive index inside and outside will not cause refraction.

Option A is correct because both the assertion and reason are true, and the reason correctly explains why the sky appears blue due to scattering.

Option C (Both primary and secondary rainbows are virtual images) is correct because rainbows are formed by refraction and reflection of sunlight, creating virtual images.

Option C (Be virtual and of the same size as the object) is correct because when the radii of curvature tend to infinity, the lens behaves like a plane glass sheet, forming a virtual image of the same size.

Option D (0.8 cm towards the mirror) is correct because the image shift is calculated using the magnification formula and the object's displacement.

Option D is correct because the focal length of a mirror is independent of the surrounding medium, and the radius of curvature is indeed twice the focal length.

Option B (If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion) is correct because while both statements are true, increased magnification is not the primary reason for using multicomponent lenses.

Option C ($\pi$) is correct because when light waves reflect from a denser medium (glass) to a rarer medium (air), there is a phase change of $\pi$ radians (180 degrees).

Option A is correct because both statements are true: concave lenses can form real images under specific conditions, and real images are formed in the direction of the light ray with respect to the lens.

Option A (0.268) is correct because the dispersive power is calculated using the deviations of red, yellow, and violet colors, and the formula yields approximately 0.268.

Option C is correct because total internal reflection occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle.

Option C (The ratio of the focal length of the objective and eyepiece) is correct because the magnifying power of a refracting telescope is given by the ratio of the objective's focal length to the eyepiece's focal length when both object and image are at infinity.

Option A (Concave lens) is correct because concave lenses diverge light rays, correcting the focusing issue in myopic eyes.

Option A ($2\,\,cm$) is correct because the length of the image is calculated using the magnification formula for a concave mirror.

Option C ($\sqrt{\frac{\mu_0-\sin \theta}{k}}$) is correct because the distance is found by setting the refractive index at the reflection point equal to the sine of the incident angle.

Option A (Total internal reflection) is correct because optical fibers rely on total internal reflection to transmit signals.

Option A (${f_0}$ should be large and ${f_e}$ should be small) is correct because the magnifying power of a telescope is directly proportional to the focal length of the objective lens and inversely proportional to the focal length of the eyepiece.

Option C ($-160 {~cm}$) is correct because it applies the lens maker's formula to calculate the focal length in a liquid, considering the refractive indices of the lens and the liquid.

Option A ($\sqrt 2$) is correct because it is calculated using the formula for the refractive index of a prism at minimum deviation, substituting the given values for the prism angle and the angle of minimum deviation.

Option B is correct because both the assertion and reason are true, but the reason does not explain the assertion. The assertion is about the minimum distance between a real object and its real image formed by a convex lens, while the reason is about the image formation by convex mirrors and concave lenses.

Option B (Emission spectrum) is correct because the spectrum from a sodium vapor lamp consists of discrete bright lines, which is characteristic of an emission spectrum.