Assertion (A): Keeping a point object fixed, if a plane mirror is moved, the image will also move.
Reason (R): In case of a plane mirror, distance of object and its image is equal from any point on the mirror.
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 image position is relative to the mirror, so it moves with the mirror. Reason (R) is true as per the property of plane mirrors, where \(OP = IP\). (R) correctly explains (A) as image movement maintains this property.
Assertion (A): If there is relative motion between a point object & a plane mirror then there must be relative motion between object and image formed by mirror.
Reason (R): If the gap between object and mirror will change, the gap between object and image remains 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
View Answer
Assertion A is true because if the object moves relative to the mirror, its image also moves, causing relative motion between object and image. Reason R is false because for a plane mirror, the object-image gap is twice the object-mirror gap, so if the object-mirror gap changes, the object-image gap also changes.
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 parallel beam of light travelling in air can be displaced laterally by a parallel transparent slab by distance more than the thickness of the plate.
Reason (R): The lateral displacement of light travelling in air increases with fall in value of refractive index of slab.
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
Assertion A is false as the lateral displacement of light through a parallel slab is always less than or equal to its thickness. Reason R is false because lateral displacement decreases as the refractive index of the slab falls.
Assertion (A): A virtual image formed by plane mirror may be inverted.
Reason (R): Longitudinal magnification in this case of plane mirror is \(-1\).
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
Assertion A is true because a plane mirror forms a laterally inverted image. Reason R is true because for a plane mirror, longitudinal magnification \(m_L = - (v/u)^2 = -1\). However, longitudinal magnification does not explain lateral inversion.
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
View Answer
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): Biconvex lens can form virtual image of a virtual object.
Reason (R): Nature of lens depends on refractive index of surrounding.
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
A biconvex lens can form a virtual image of a virtual object. The nature of a lens (converging/diverging) depends on the refractive index of the lens material relative to the surrounding medium. Therefore, both A and R are true, and R is the correct explanation of A.
Assertion (A): The minimum length of mirror required to form complete image of man of height \(H) is \(H/2\).
Reason (R): Image of an object is obtained if incident light ray reaches the reflecting surface.
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 minimum length of a plane mirror to see a full image of a person of height \(H) is \(H/2\). Image formation occurs when light rays reach and reflect from a surface. Both statements are true, but R is a general principle and does not explain the specific \(H/2\) relation.
Assertion (A): Concave mirror can not form real image of real object.
Reason (R): Concave mirror behave as a diverging mirror.
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
A concave mirror is a converging mirror and can form real images of real objects when the object is beyond the focal point. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): Radius of curvature of a concave mirror is \(20 \text{cm}\). If a real object is placed in front of a mirror at \(10 text{cm}\) from pole of the mirror, image is formed at infinity.
Reason (R): When object is placed at focus of a converging optical system then its image is formed at infinity.
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 a concave mirror, \(R = 20 \text{cm}\), so \(f = R/2 = 10 \text{cm}\). An object placed at the focal point of a converging mirror forms its image at infinity. Both A and R are true, and R correctly explains A.