An object is placed on the principal axis of a concave mirror of focal length 10 cm at a distance of 8 cm from the pole. Find position and nature of the image :
A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at :
Mark the correct options :
Which of the following (referred to a spherical mirror) depend on whether the rays are paraxial or not ?
The image of an object placed perpendicular to the principal axis of a mirror, will be erect if :
A point object is moving towards a concave mirror of focal length \(25\text{ cm}\). When it is at a distance of \(20\text{ cm}\) from the mirror, its velocity is \(5\text{ cm/sec}\). Find velocity of image at that instant :-
Using the relation between object and image velocity: \(v_i = -m^2 v_o\). Here, magnification \(m = \frac{f}{f-u} =\frac{-25}{-25 - (-20)} = 5\). Hence, \(v_i = -5^2 \times 5 = -125\text{ cm/s}\). The speed is \(125\text{ cm/s}\).
Assertion (A): Concave mirror can not form real image of real object.
Reason (R): Concave mirror behave as a diverging mirror.
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.
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.
Assertion (A): In telescopes objective lens is taken of large diameter or aperture.
Reason (R): Larger aperture remove spherical aberration.
A large diameter objective lens in telescopes increases the light-gathering power and improves resolving power, allowing observation of fainter and finer details. Hence, Assertion (A) is true. However, spherical aberration generally *increases* with larger apertures, as rays further from the principal axis are not focused at the same point. Thus, Reason (R) is false.
Assertion (A): In case of a concave mirror if a point object is moving towards the mirror along its principal axis then its image will always move away from the mirror.
Reason (R): In case of reflection (along the principal axis of mirror) object and image always travel in same directions.
For a concave mirror, if an object moves from infinity towards the center of curvature (C), its real image moves from the focus (F) to C, thus moving *towards* the mirror. So, Assertion (A) is false. Also, the object and image do not *always* travel in the same direction along the principal axis; their relative motions depend on the object's position relative to F and C. Hence, Reason (R) is also false. Both A and R are false.