. A certain microscope is provided with objectives that have...

. A certain microscope is provided with objectives that have focal lengths of $16 \mathrm{mm}, 4 \mathrm{mm}$ , and 1.9 $\mathrm{mm}$ and with eye pieces that have angular magnifications of $5 \times$ and $10 \times$ Each objective forms an image 120 $\mathrm{mm}$ beyond its second focal point. Determine (a) the largest overall angular magnification obtainable and (b) the smallest overall angular magnification obtainable.

. A certain microscope is provided with objectives that have focal lengths of $16 \mathrm{mm}, 4 \mathrm{mm}$ , and 1.9 $\mathrm{mm}$ and with eye pieces that have angular magnifications of $5 \times$ and $10 \times$ Each objective forms an image 120 $\mathrm{mm}$ beyond its second focal
point. Determine (a) the largest overall angular magnification obtainable and (b) the smallest overall angular magnification obtainable.

Key Concepts

Focal Length

Focal length is the distance between the center of a lens and its focus, where parallel rays of light converge after passing through the lens. It is a fundamental property of lenses and determines the degree of light convergence or divergence, impacting the size and clarity of the image produced by the optical system.

Objective Lens

The objective lens is the primary optical component in a microscope that collects light from the specimen and forms an intermediate image. Its focal length directly influences the linear magnification of the system, which is the first step in the overall magnification process.

Eyepiece (Ocular)

The eyepiece, or ocular lens, is the lens through which the viewer observes the intermediate image formed by the objective. It provides additional angular magnification, further enlarging the image and making it more accessible to the human eye.

Angular Magnification

Angular magnification refers to the ratio by which an optical instrument increases the apparent angular size of an object. In microscopes, it is determined by both the magnifying power of the eyepiece and, in combination with the objective, defines the overall magnification experienced by the observer.

Overall Magnification

Overall magnification in a microscope is the product of the magnifications of the objective lens and the eyepiece. This combined effect determines how much larger the specimen appears compared to its actual size, and it encapsulates both the linear magnification provided by the objective and the angular magnification of the ocular component.

Transcript

00:01 All right, so for this question, it was asking us, what is the largest overall magnification? okay, so we know since we want to care about the value of magnification, we can just simply put absolute value on m here.

00:19 M here stands for the magnification, which is equal to absolute value minus v over you, which is equal to absolute value of v over you, okay? b is the image distance, u is the object distance.

00:35 So in this question, you were saying that each object lens is forming an image 120 millimeter beyond its second focal point.

00:43 Okay? so the image distance formed by the objective lens is much larger when compared to the focal lens.

00:50 And this only happens when the object distance is nearly equal to the focal lens of the lens, which means that we basically need to consider the object distance is equal to the focal length.

01:03 So now we have such an equation which is absolute value m equal to v over f.

01:10 So now let's start plugging all different focal lens and the image distance to find out different magnification number.

01:19 Okay? so well just want to let you guys know image distance here is equal to the distance apart, let's say l, plus the focal lens.

01:31 Okay? and in the question you were saying it's 120 millimeter beyond.

01:37 Okay? so it's 120 millimeter plus the whatever focal lens you had.

01:45 Okay? so first, let's focus on the focal lens of 16 millimeter.

01:51 So we got m1 is equal to, you want to put absolute value, that is totally fine.

02:01 With a v which is 120 millimeter plus 16 millimeter over 16 millimeter and this will give us the values about 8 .5.

02:26 So for the focal lens with 4 millimeter it will have a magnification number of b over f which is 120 millimeter plus 4 millimeter over 4 millimeter and this will give us 31 for the magnification number and the magnification number for the focal lens of 1 .9 mm -upre 1 .9 millimeter will give us v which is 120 millimeter plus 1 .9 millimeter over the focal lens which is 1 .9 millimeter and this will give us about 64 .16.

03:31 Okay? so now we know that comparing with all these focal lens, the magnification number is the largest when the focal lens is 1 .9 millimeter.

03:45 Okay? let me use here.

03:47 So this is the largest...

Please give Ace some feedback