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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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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.
Assertion (A): Iris of the eye contains rods and cones which transmits electric signal to brain through optic nerve.
Reason (R): Rods sense colour of object and cone sense intensity of light.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Both Assertion (A) and Reason (R) are false. Rods and cones are located in the retina, not the iris. Rods detect light intensity (dim light), and cones detect color (bright light).
Assertion (A): When two thin equiconvex lens are placed in contact, the effective power of combination may decrease.
Reason (R): Power of lens is defined as ability of bending of light.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
For two thin lenses in contact, the equivalent power is \(P = P_1 + P_2\). For equiconvex lenses, both \(P_1\) and \(P_2\) are positive. Therefore, the effective power (P) will always increase, not decrease. Thus, (A) is false.
Power of a lens is indeed a measure of its ability to bend or converge/diverge light rays. Thus, (R) is true.
Therefore, (A) is false but (R) is true.
Assertion (A): Lens formula can be applied only for thin lenses.
Reason (R): For thick lenses one cannot find image position.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
The simple lens formula \(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\) is an approximation valid for thin lenses. Thus, (A) is true.
For thick lenses, more complex formulae or ray tracing methods are used, but the image position can certainly be found. Thus, (R) is false.
Therefore, (A) is true but (R) is false.