Lenses and Optical Instruments

[withthemotive]

1.
A diverging lens with a focal length of -14 cm is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33cm to the left of the converging lens.

Where will the final image be located.


2.
1/f = 1/di + 1/do
dob = L - dia


3.
After solve for the converging lens (a), the dia was 39.6cm. Then, to get the object distance from the diverging lens(b), the length between was subtracted from the image distance from (a). dob = 12-39.6 = -27.6

I then solve for the object distance for the diverging lens and get a negative value. -28.4cm.
It this correct? If so, is it simply just 28.4 cm BEHIND the diverging lens?

 

[Redbelly98]

Looks right. The negative number indicates a virtual image, i.e. it is to the left of the diverging lens.

 

[nlightner]

I would like to clarify some information and provide a response to the given content.

Firstly, it is important to note that lenses and optical instruments are used to manipulate and focus light, allowing us to see objects clearly. They are widely used in various fields such as physics, astronomy, and medicine.

In the given scenario, we are dealing with two lenses - a diverging lens and a converging lens. A diverging lens is a lens that spreads out light rays, while a converging lens is a lens that brings light rays together. These lenses have different focal lengths, which determine their ability to bend light.

According to the given information, the diverging lens has a focal length of -14 cm, which means it has a negative focal length. This indicates that it is a diverging lens, and the image formed by this lens will always be virtual and upright. On the other hand, the converging lens has a positive focal length of 18 cm, indicating that it is a converging lens, and the image formed by this lens can be real or virtual depending on the object's position.

Using the lens formula, 1/f = 1/di + 1/do, we can calculate the image distance (di) for the converging lens. Plugging in the values, we get di = 39.6 cm. This means that the image formed by the converging lens is located 39.6 cm to the right of the lens.

Next, to find the object distance for the diverging lens, we can use the formula dob = L - dia, where L is the distance between the two lenses. In this case, L = 12 cm. Substituting the values, we get dob = -27.6 cm. This means that the object distance for the diverging lens is -27.6 cm, which is a negative value.

It is important to note that a negative object distance indicates that the object is located behind the lens. In this case, the object is located 27.6 cm behind the diverging lens, and the final image formed by this lens will be located at this point. Therefore, the final image will be located 28.4 cm behind the diverging lens.

In conclusion, the calculations are correct, and the final image will be located 28.4 cm behind the diverging lens. It is important to pay attention to the signs and values when dealing with lenses