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यदि +4 D शक्ति का एक उत्तल लेंस और -10D शक्ति का एक अवतल लेंस एक दूसरे के संपर्क में रखा जाता है, परिणामी शक्ति क्या होगी ?
6 D
+14 D
+6 D
14 D
उपर्युक्त में से कोई नहीं
6 D
The correct answer is -6 D . Key Points The power of a lens is defined as the reciprocal of its focal length in meters: P = 1/f (in meters) . When two lenses are placed in contact with each other, their resultant power is the algebraic sum of their individual powers: P(resultant) = P1 + P2 . Here, the power of the convex lens (P1) is +4 D, and the power of the concave lens (P2) is -10 D. Resultant power = +4 D + (-10 D) = -6 D. A negative power indicates that the combined system behaves as a concave lens, which is diverging in nature. Additional Information Convex Lens (+4 D): A convex lens is a converging lens that brings parallel rays of light to a focus. Its power is positive, indicating that it produces a real and inverted image if the object is placed beyond the focal point. In this case, the convex lens has a power of +4 D, which corresponds to a focal length of 0.25 m (f = 1/P). Concave Lens (-10 D): A concave lens is a diverging lens that causes parallel rays of light to spread out as if they were emanating from a virtual focal point. Its power is negative, indicating that it produces a virtual and upright image. In this case, the concave lens has a power of -10 D, which corresponds to a focal length of -0.1 m (f = 1/P). Resultant Lens Behavior: The resultant power of the lens system is -6 D, meaning the system behaves like a concave lens with a focal length of -0.1667 m. This combined lens system would diverge light rays, as indicated by the negative resultant power.
The correct answer is -6 D..
When two lenses are placed in contact with each other, their resultant power is the algebraic sum of their individual powers: P(resultant) = P1 + P2.
Here, the power of the convex lens (P1) is +4 D, and the power of the concave lens (P2) is -10 D.
Resultant power = +4 D + (-10 D) = -6 D.
A negative power indicates that the combined system behaves as a concave lens, which is diverging in nature.:
A convex lens is a converging lens that brings parallel rays of light to a focus.
Its power is positive, indicating that it produces a real and inverted image if the object is placed beyond the focal point.
In this case, the convex lens has a power of +4 D, which corresponds to a focal length of 0.25 m (f = 1/P).
Concave Lens (-10 D):
A concave lens is a diverging lens that causes parallel rays of light to spread out as if they were emanating from a virtual focal point.
Its power is negative, indicating that it produces a virtual and upright image.
In this case, the concave lens has a power of -10 D, which corresponds to a focal length of -0.1 m (f = 1/P).
Resultant Lens Behavior:
The resultant power of the lens system is -6 D, meaning the system behaves like a concave lens with a focal length of -0.1667 m.
This combined lens system would diverge light rays, as indicated by the negative resultant power.
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