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A concave lens has focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also find the magnification of the lens.

Physics

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Answer

30 cm30 \text{ cm}

0.33

Step-by-step solution

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Q:12 A concave lens has focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also find the magnification of the lens.

  1. Identify the given values and apply sign conventions.

    For a concave lens:

    • Focal length (ff) is negative. So, f=−15 cmf = -15 \text{ cm}.
    • The image formed by a concave lens is always virtual and on the same side as the object. So, the image distance (vv) is negative. v=−10 cmv = -10 \text{ cm}.
  2. Calculate the object distance (uu) using the lens formula.

    The lens formula is:

    1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

    Rearrange the formula to solve for 1u\frac{1}{u}:

    1u=1f−1v\frac{1}{u} = \frac{1}{f} - \frac{1}{v}

    Substitute the values:

    1u=1−15 cm−1−10 cm\frac{1}{u} = \frac{1}{-15 \text{ cm}} - \frac{1}{-10 \text{ cm}} 1u=−115 cm+110 cm\frac{1}{u} = -\frac{1}{15 \text{ cm}} + \frac{1}{10 \text{ cm}}

    Find a common denominator, which is 30:

    1u=−230 cm+330 cm\frac{1}{u} = -\frac{2}{30 \text{ cm}} + \frac{3}{30 \text{ cm}} 1u=130 cm\frac{1}{u} = \frac{1}{30 \text{ cm}} u=30 cmu = 30 \text{ cm}
  3. Calculate the magnification (MM) of the lens.

    The magnification formula is:

    M=−vuM = -\frac{v}{u}

    Substitute the values:

    M=−−10 cm30 cmM = -\frac{-10 \text{ cm}}{30 \text{ cm}} M=1030M = \frac{10}{30} M=13M = \frac{1}{3} M≈0.33M \approx 0.33

    The object should be placed at a distance of 30 cm\boxed{30 \text{ cm}} from the lens.
    The magnification of the lens is 0.33\boxed{0.33}.

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