if the height of the object in the previous problem is 1.2cm , what will be the height of the image ?

To determine the height of the image when the height of the object is given as 1.2 cm, we need to consider the context of the problem, such as the type of optical system involved—like a lens or a mirror—and the relevant formulas. Let's break this down step by step.

Understanding Image Formation

In optics, the height of the image can be calculated using the magnification formula, which relates the height of the object to the height of the image. The formula for magnification (M) is given by:

• M = (Height of Image) / (Height of Object)
• M = (Image Distance) / (Object Distance)

From these equations, we can see that if we know the magnification and the height of the object, we can easily find the height of the image.

Calculating the Height of the Image

Let’s say we have a magnification value from the previous problem. For example, if the magnification is 2, this means the image is twice the height of the object. Given that the height of the object is 1.2 cm, we can calculate the height of the image as follows:

Height of Image = Magnification × Height of Object

Substituting the values:

Height of Image = 2 × 1.2 cm = 2.4 cm

Considering Different Scenarios

It's important to note that magnification can also be negative, which indicates that the image is inverted. For instance, if the magnification were -0.5, the calculation would be:

Height of Image = -0.5 × 1.2 cm = -0.6 cm

This result means the image is 0.6 cm tall and inverted. Depending on the optical system, the magnification can vary, so always check the specifics of the problem to apply the correct value.

Practical Example

Imagine you are using a concave mirror to reflect an object. If the object is placed at a distance where the magnification is known, you can apply the same principles. If the object height is 1.2 cm and the magnification is 1.5, the image height would be:

Height of Image = 1.5 × 1.2 cm = 1.8 cm

This means the image is taller than the object and upright if the magnification is positive.

Final Thoughts

In summary, to find the height of the image, you need to know the magnification factor. Once you have that, simply multiply it by the height of the object. This approach applies to various optical systems, whether they are lenses or mirrors, and helps in understanding how images are formed in different contexts.