Two objects \(A\) and \(B\)are placed at \(15\, cm\) and \(25\, cm\) from the pole in front of a concave mirros having radius of curvature \(40\, cm\). The distance between images formed by the mirror is:
Two objects \(A\) and \(B\)are placed at \(15\, cm\) and \(25\, cm\) from the pole in front of a concave mirros having radius of curvature \(40\, cm\). The distance between images formed by the mirror is:
Show Hint
Remember the sign conventions for concave mirrors. The mirror formula is essential for solving problems involving image formation.
\(40 \,cm\)
\(160 \,cm\)
\(60 \,cm\)
\(100\, cm\)
The Correct Option is B
Solution and Explanation
Step 1: Determine the Focal Length
The focal length (\(f\)) of a concave mirror is half of its radius of curvature (\(R\)):
\[ f = \frac{R}{2} = \frac{40}{2} = -20 \, \text{cm} \]
The focal length is negative for a concave mirror.
Step 2: Use the Mirror Formula for Object A
The mirror formula relates the object distance (\(u\)), image distance (\(v\)), and focal length (\(f\)):
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]
For object A, \(u_1 = -15 \, \text{cm}\) (negative because the object is in front of the mirror).
\[ \frac{1}{v_1} + \frac{1}{-15} = \frac{1}{-20} \] \[ \frac{1}{v_1} = \frac{1}{15} - \frac{1}{20} = \frac{20 - 15}{300} = \frac{5}{300} = \frac{1}{60} \] \[ v_1 = 60 \, \text{cm} \]
Step 3: Use the Mirror Formula for Object B
For object B, \(u_2 = -25 \, \text{cm}\):
\[ \frac{1}{v_2} + \frac{1}{-25} = \frac{1}{-20} \] \[ \frac{1}{v_2} = \frac{1}{25} - \frac{1}{20} = \frac{20 - 25}{500} = \frac{-5}{500} = \frac{-1}{100} \] \[ v_2 = -100 \, \text{cm} \]
Step 4: Calculate the Distance Between the Images
The image of A is formed at \(v_1 = 60 \, \text{cm}\) (positive, so it’s a real image formed in front of the mirror). The image of B is formed at \(v_2 = -100 \, \text{cm}\) (negative, so it’s a virtual image formed behind the mirror). The distance (\(d\)) between the images is:
\[ d = |v_1| + |v_2| = 60 + 100 = 160 \, \text{cm} \]
Conclusion:
The distance between the images is 160 cm (Option 2).
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Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.
Properties of Convex lens:
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Properties of Concave lens:
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- It parts the incident rays away from the principal axis.
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