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A spherical mirror diverges a beam of light, which is incident on it. Which of the following statement(s) about the mirror is/are true? i) The mirror used is convex. ii) The mirror has positive focal length. iii) The image formed by this mirror can be seen on a screen.
Both (ii) and (iii)
Only (i)
Both (i) and (ii)
Only (iii)
Both (i) and (ii)
A spherical mirror that diverges a beam of light is a convex mirror. Since it is a convex mirror, its focus lies behind the mirror, giving it a positive focal length (f>0). Convex mirrors always form virtual, erect, and diminished images, which cannot be projected onto a screen.
A spherical mirror that diverges a beam of light is a convex mirror. Since it is a convex mirror, its focus lies behind the mirror, giving it a positive focal length (f>0). Convex mirrors always form virtual, erect, and diminished images, which cannot be projected onto a screen.
Think of a convex mirror as the rearview mirror in your car; it spreads out the view behind you to show a wider area, but the image you see is inside the mirror, not out on the road.
Convex is 'Diverging' (CD) and has a 'Positive' (P) focal length. Remember: CD-P (Convex, Diverging, Positive).
f1тАЛ=v1тАЛ+u1тАЛ тАФ Mirror Formula
m=тИТuvтАЛ тАФ Magnification Formula
When parallel rays of light strike a convex mirror, they reflect outward, diverging away from each other. Because the rays appear to originate from a point behind the mirror, the focal point is virtual, and the focal length is defined as positive according to the Cartesian sign convention. Since the rays never actually meet in front of the mirror, a real image cannot be formed, making it impossible to capture the image on a screen.
Convex mirrors are also known as diverging mirrors.
A convex mirror always produces a virtual, erect, and diminished image.
Virtual images cannot be obtained on a screen.
The focal length (f) of a convex mirror is positive.
Provides a wider field of view compared to plane mirrors.
Useful for security and rearview mirrors in vehicles.
Does not form a real image that can be projected.
Objects appear smaller and further away than they actually are.
Vehicle rearview mirrors
Security mirrors in shops and blind turns
The statement (i) 'The mirror used is convex' is the definition given in the question, so it is true. Statement (ii) 'The mirror has positive focal length' is true for a convex mirror. Statement (iii) 'The image formed by this mirror can be seen on a screen' is false because convex mirrors only form virtual images.
The official answer identifies the combination of true statements.
C is correct тАФ Since the mirror is convex, it has a positive focal length, but it cannot form a real image on a screen.
Always remember: Real images are inverted (formed by concave mirrors), while virtual images are erect (formed by plane, convex, and concave mirrors).
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