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Task One: Methods of producing a magnet

Here are different methods to produce a magnet:

  • Single Touch Method: This involves rubbing a piece of magnetic material (like steel) with one pole of a permanent magnet, always in the same direction.
  • Double Touch Method: In this method, two permanent magnets are used to stroke a piece of magnetic material. The magnets are stroked from the center outwards towards the ends, with opposite poles touching the material.
  • Electrical Method (Electromagnetism): This method involves passing an electric current through a coil of wire wound around a ferromagnetic core.
  • Induction Method: This involves placing a magnetic material near a strong magnet. The material will become temporarily magnetized by induction.

Task Two:

We are given two mirrors: a concave mirror and a convex mirror, both with a focal length of 20 cm20 \text{ cm}. A person of height 4 cm4 \text{ cm} is standing 25 cm25 \text{ cm} away from each mirror.

Part a· 2 steps

**Which mirror forms a bigger image?

Given Data:
Object height, ho=4 cmh_o = 4 \text{ cm}
Object distance, u=25 cmu = 25 \text{ cm}
Focal length of concave mirror, fc=+20 cmf_c = +20 \text{ cm}
Focal length of convex mirror, fx=−20 cmf_x = -20 \text{ cm} (for a convex mirror, ff is negative)

  1. Calculate the image distance (vv) and image height (hih_i) for the concave mirror.

    We use the mirror formula: 1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

    120=1vc+125\frac{1}{20} = \frac{1}{v_c} + \frac{1}{25} 1vc=120−125=5−4100=1100\frac{1}{v_c} = \frac{1}{20} - \frac{1}{25} = \frac{5-4}{100} = \frac{1}{100} vc=100 cmv_c = 100 \text{ cm}

    Magnification, M=−vu=hihoM = -\frac{v}{u} = \frac{h_i}{h_o}

    Mc=−10025=−4M_c = -\frac{100}{25} = -4

    Image height, h_{ic} = M_c \times h_o = -4 \times 4 \text{ cm} = -16 \text{ cm} $$ The magnitude of the image size is 16 \text{ cm}$. The negative sign indicates an inverted image.

    Step 2: Calculate the image distance (vv) and image height (hih_i) for the convex mirror.
    We use the mirror formula: 1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

    1−20=1vx+125\frac{1}{-20} = \frac{1}{v_x} + \frac{1}{25} 1vx=−120−125=−5−4100=−9100\frac{1}{v_x} = -\frac{1}{20} - \frac{1}{25} = \frac{-5-4}{100} = \frac{-9}{100} vx=−1009 cm≈−11.11 cmv_x = -\frac{100}{9} \text{ cm} \approx -11.11 \text{ cm}

    Magnification, M=−vu=hihoM = -\frac{v}{u} = \frac{h_i}{h_o}

    Mx=−(−100/9)25=1009×25=49M_x = -\frac{(-100/9)}{25} = \frac{100}{9 \times 25} = \frac{4}{9}

    Image height, h_{ix} = M_x \times h_o = \frac{4}{9} \times 4 \text{ cm} = \frac{16}{9} \text{ cm} \approx 1.78 \text{ cm} $$ The magnitude of the image size is approximately 1.78 \text{ cm}$. The positive sign indicates an upright image.

  2. Compare the image heights.

    The image height from the concave mirror is 16 cm16 \text{ cm}.
    The image height from the convex mirror is 1.78 cm1.78 \text{ cm}.

    Conclusion:
    The mirror that forms a bigger image is the concave mirror.

    The concave mirror forms a bigger image.\boxed{\text{The concave mirror forms a bigger image.}}

Part b· 3 steps

**Write a brief report about the nature of the image formed by each mirror and advise which mirror is suitable for use as a driving mirror.

  1. Characteristics of the image formed by a concave mirror.

    For an object placed 25 cm25 \text{ cm} from a concave mirror with f=20 cmf = 20 \text{ cm} (i.e., the object is between F and C):

    • The image is real.
    • The image is inverted.
    • The image is magnified.
    • The image is formed in front of the mirror, beyond the center of curvature (C).
  2. Characteristics of the image formed by a convex mirror.

    For any real object placed in front of a convex mirror:

    • The image is virtual.
    • The image is erect (upright).
    • The image is diminished (smaller).
    • The image is formed behind the mirror, between the pole and the focus.
  3. Advice on which mirror is suitable for use as a driving mirror.

    A driving mirror needs to provide a wide field of view and form erect images so that objects appear in their correct orientation.

    • Concave mirrors form inverted images when the object is far from the focus, which is unsuitable for driving. They also have a narrow field of view.
    • Convex mirrors always form erect, diminished, and virtual images, and they provide a much wider field of view. This allows the driver to see a larger area behind the vehicle.

    Therefore, a convex mirror is more suitable for use as a driving mirror.

    A convex mirror is more suitable for use as a driving mirror.\boxed{\text{A convex mirror is more suitable for use as a driving mirror.}}
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