The object is moved to 4cm from the same lens. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

To calculate the distance to the image (di), magnification (m), and height of the image (hi), you can use the lens formula, magnification formula, and image height formula:

1. Lens formula: [ \frac{1}{f} = \frac{1}{do} + \frac{1}{di} ]
2. Magnification formula: [ m = -\frac{di}{do} ]
3. Image height formula: [ hi = m \times ho ]

where:

• ( f ) is the focal length of the lens,
• ( do ) is the object distance,
• ( di ) is the image distance,
• ( m ) is the magnification,
• ( ho ) is the object height.

Plug in the known values to find ( di ), ( m ), and ( hi ).

To calculate the distance to the image from the lens ((d_i)), the magnification ((M)), and the height of the image ((h_i)), you can use the thin lens equation and the magnification equation.

1. Thin lens equation: [ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ]

2. Magnification equation: [ M = \frac{h_i}{h_o} = -\frac{d_i}{d_o} ]

Given:

• (d_o = -4 , \text{cm}) (since the object is placed 4 cm from the lens)
• (f) (the focal length of the lens)

You can solve these equations simultaneously to find (d_i) and (M). Then, once you have (M), you can find (h_i) using the object height ((h_o)).

Steps:

1. Use the thin lens equation to find (d_i).
2. Substitute the value of (d_i) into the magnification equation to find (M).
3. Use the magnification (M) to find (h_i) using the object height (h_o).

Remember to pay attention to the signs of distances ((d_i) and (d_o)) and magnification ((M)):

• If the image is formed on the same side as the object, the distance is negative.
• If the image is upright, magnification is positive. If it is inverted, magnification is negative.

Once you find (d_i), (M), and (h_i), you can substitute the values to calculate each parameter.