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(ii). A girl was playing with a thin beam of light from a laser torch by directing it from different directions on a convex lens vertically. She was surprised to see that in a particular direction, the beam of light continued to move along the same direction after passing through the lens. State the reason for her observation. Draw a ray diagram to support your answer.

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(i). We are given that the lens produces a magnification of \[ - 0.5\]. We know that a concave lens does not have a negative magnification and only convex lenses have negative magnification. A convex lens is converging in nature.

Hence, the given lens is converging.

We are given in the problem

\[f = + 6cm\]

\[m = - 0.5\]

We know that,

\[m = \dfrac{v}{{\left( { - u} \right)}} = - 0.5\]

\[v = + 0.5u\]

We know by the lens formula

\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]

\[\Rightarrow \dfrac{1}{6} = \dfrac{1}{{0.5u}} - \dfrac{1}{{\left( { - u} \right)}}\]

\[\Rightarrow \dfrac{1}{6} = \dfrac{1}{{0.5u}} + \dfrac{1}{{\left( { u} \right)}}\]

Now on taking LCM,

\[\Rightarrow \dfrac{1}{6} = \dfrac{1+0.5}{{0.5u}}\]

\[\Rightarrow \dfrac{1}{6} = \dfrac{3}{{u}}\]

\[\Rightarrow u = 18cm\]

\[\therefore v = 0.5u = 9cm\]

The diagram of the given situation is given below

(ii). In the problem, we are told that the girl points a laser towards a convex lens that is held vertically. If she points in a particular direction the beam of light does not get refracted. This situation can only occur if the laser is directly pointed at the optical center. Any light ray that strikes at the optical center passes through without any refraction.

The diagram of the given situation is given below