Assertion (A): A simple microscope may have different magnification for different persons.
Reason (R): All persons must have the same near point distance of \(25\text{ cm}\).
Assertion (A) is true as magnification depends on individual near point, which varies. Reason (R) is false as the near point varies for different individuals and is not universally \(25\text{ cm}\).
Assertion (A): If an object placed on the optic axis of a lens is illuminated by white light, then image formed will be coloured and not exactly white.
Reason (R): The lens has different focal lengths for different colours.
Assertion (A) is true due to chromatic aberration. Reason (R) is true and correctly explains (A) because the refractive index of lens material varies with wavelength, causing different focal lengths for different colors.
Assertion (A): Paraxial rays are always parallel to the principal axis.
Reason (R): A parallel beam parallel to principal axis converges at the focal point.
Assertion (A) is false; paraxial rays are simply close to the axis, not necessarily parallel. Reason (R) is also false because due to spherical aberration, a real parallel beam does not perfectly converge to a single focal point.
Assertion (A): The image focus (\(2^{\text{nd}}\) focus) and the object focus (\(1^{\text{st}}\) focus) are on the opposite side of the biconvex or biconcave lens.
Reason (R): The radii of curvature of a biconvex lens and biconcave lens are on the opposite side of the lens.
Assertion (A) is true; the two principal focal points are on opposite sides of the lens. Reason (R) is true, describing the geometric arrangement of the centers of curvature. However, (R) does not explain (A).
Assertion (A): A lens has two principal focal lengths which may be different in magnitude.
Reason (R): The distance of both principal focus from optical centre of lens depend on the two radii of curvature of the lens. Distance of both principal focus from optical centre a lens are same only if radii of curvature of both sides of lens are same.
Assertion (A) is true if the lens is in different media on either side. Reason (R) is false because for a thin lens in the same medium, magnitudes of focal lengths are always equal, irrespective of the equality of radii of curvature.
Assertion (A): When the upper half of a converging lens is missing, a real image formed by the lens for a real object will lack its lower half.
Reason (R): The real image formed by a thin lens for a real object will be always erected.
Assertion A is false because even with half the lens missing, a complete image is formed, but its intensity is reduced. Reason R is false as real images formed by a thin lens for a real object are generally inverted, not always erected.
Assertion (A): A convex lens of glass \((\mu = 1.5)\) behaves as a diverging lens when immersed in a medium of refractive index \(\mu = 1.65\).
Reason (R): A diverging lens is thinner in the middle and thicker at the edges.
Assertion A is true; if \(mu_{medium} > \mu_{lens}\), a convex lens becomes diverging due to sign change in the lens maker's formula. Reason R is true as it describes a typical concave (diverging) lens shape. But the shape of a diverging lens does not explain the behavioral change of a convex lens.
Assertion (A): An object placed at a distance less than \(25 \text{ cm}\), in front of a normal eye. The image of this object on retina is blurred.
Reason (R): Image is formed before retina.
The near point for a normal eye is \(25 \text{ cm}\), meaning objects closer than this cannot be focused clearly on the retina. So, Assertion (A) is true. However, for a normal eye attempting to focus on an object closer than its near point, the image would effectively form *behind* the retina if the lens power is insufficient, not before it. Thus, Reason (R) is false.
Assertion (A): In displacement method of finding focal length of a convex lens, if magnification in a position of lens is \( -2 \), then magnification in another position of lens should be \( -1/2 \).
Reason (R): This method can not be applied for diverging lens.
In the displacement method, if magnifications are \( m_1 \) and \( m_2 \) for two positions, then \( m_1 m_2 = 1 \). If \( m_1 = -2 \), then \( m_2 = -1/2 \). The method requires formation of real images, which diverging lenses cannot produce for real objects.
Assertion (A): Secondary rainbow is fainter than primary rainbow.
Reason (R): Secondary rainbow is seen due to the scattering of primary rainbow through water molecules.
Assertion (A) is true; secondary rainbows are fainter due to two internal reflections causing more light loss. Reason (R) is false; secondary rainbows result from light undergoing two internal reflections in raindrops, not scattering of a primary rainbow.