JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Curved Surfaces

  • question_answer
    A 35 mm film is to be projected on a 20 m wide screen situated at a distance of 40 m from the film-projector. Calculate the focal length of projection lens.

    A) 70 mm

    B) 35 mm

    C) 40 mm

    D) 20 mm

    Correct Answer: A

    Solution :

    As in case of projector, \[m=\frac{I}{O}=\frac{v}{u}\]
    So,       \[-\frac{20\times 100\,cm}{3.5\,cm}=\frac{40\times 100}{u}\]
    i.e.,       \[u=-7\text{ }cm\]
    i.e., film is at a distance of 7 cm in front of projection lens.
    And from lens formula \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f},\] here we have  \[\frac{1}{4000}-\frac{1}{-7}=\frac{1}{f}\] or \[\cong 7\,cm=70\,mm\]
    [as (1/4000) << (1/7)]
    i.e., focal length of projection lens is 70 nun.

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