A small object is placed $$50$$ cm to the left of a thin convex lens of focal length $$30cm$$. A convex spherical mirror of radius of curvature $$100$$ cm placed to the right of the lens at a distance of $$50$$ cm. The mirror is tilted such that the axis of the mirror is at an angle θ$$=300$$ to the axis of the lens, as shown in the figureIf the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in$$ $$cm) of the point (x$$, $$y) at which the image is formed are

Question

A small object is placed $$50$$ cm to the left of a thin convex lens of focal length $$30cm$$. A convex spherical mirror of radius of curvature $$100$$ cm placed to the right of the lens at a distance of $$50$$ cm. The mirror is tilted such that the axis of the mirror is at an angle θ$$=300$$  to the axis of the lens, as shown in the figureIf the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in$$ $$cm) of the point (x$$, $$y) at which the image is formed are

Infinity Learn · Accepted Answer

For lens,$$1f=1v$$−$$1u$$⇒$$130=1v$$−$$1$$−$$50$$⇒$$v=75cm$$ Distance of this image $$I1$$ from pole of mirror along principal axis $$=75$$−$$50=25cm$$ Mirror formula. if mirror is not rotated $$1f=1v+1u$$⇒$$150=1v+125$$⇒$$v=$$−$$50cm$$ The image I would have formed as shown had the mirror been straight.  But here the mirror is tilted by $$30$$∘ . So, the image will be tilted by $$60$$∘ and will be formed at A . $$MA=50cos$$⁡$$60$$∘$$=25cmI$$′$$A=50sin$$⁡$$60$$∘$$=253cm$$ Since, origin is the center of lens, so coordinates, $$x=OM$$−$$AM=50$$−$$25=25cmy=l$$′$$A=253cm$$

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