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#geometry

7 public questions tagged with this topic.

Telescope, Human Eye and Defects of Vision

A prism of refracting angle \( 50^\circ \) has a minimum deviation of \( 25^\circ \). What is the refractive index?

**Telescope resolving power** depends on objective aperture, magnification limited by objective diffraction, terrestrial telescope adds erecting lens, Galilean uses diverging eyepiece for erect image, reflecting telescope uses concave mirror objective avoiding chromatic aberration. Refractive index: n = (sin ( (A + D_m/2) )/sin ( (A/2) )) . A = 50° , D_m = 25° . n = (sin ( (50 + 25/2) )/sin ( (50/2) )) = (sin 37.5°/sin 25°) . sin 37.5° ≈ 0.609 , sin 25° ≈ 0.423 . n = (0.609/0.423) ≈ 1.44 . Substituting values gives 1.44, which matches expected image position and magnification from mirror/lens

Ref: NCERT > Physics Book > Ray Optics > Telescope, Human Eye and Defects of Vision

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Vector Product and Rotational Kinematics

A uniform triangular lamina has vertices at (0,0), (5,0), and (0,6). What is the x-coordinate of its center of mass?

For a uniform triangular lamina, the center of mass is at the centroid, the average of the vertices. X = 0+5+03 = 53≈1.67m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.67 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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