part h: application
1. a forensics lab technician is trying to solve an atm robbery. they have a picture of the suspect from the bank camera, but even when the photo is enlarged, the face is too blurry to use for identification. explain why the image is blurry when enlarged.

2. if a field of view is 5.0 mm at 60×, what is the field of view at 25×?

3. if you are using your microscope, and a specimen takes up 1/3 of the field of view at 1000×, what is its diameter?

4. a student viewed the letter “e” on a slide. the student could clearly see the letter when using the 4× and 10× objectives, but when the 40× objective was used, the “e” was no longer visible. give several possible reasons for this result.

Question

part h: application
1. a forensics lab technician is trying to solve an atm robbery. they have a picture of the suspect from the bank camera, but even when the photo is enlarged, the face is too blurry to use for identification. explain why the image is blurry when enlarged.

2. if a field of view is 5.0 mm at 60×, what is the field of view at 25×?

3. if you are using your microscope, and a specimen takes up 1/3 of the field of view at 1000×, what is its diameter?

4. a student viewed the letter “e” on a slide. the student could clearly see the letter when using the 4× and 10× objectives, but when the 40× objective was used, the “e” was no longer visible. give several possible reasons for this result.

Accepted Answer

### Question 1
# Brief Explanations:
Images from cameras (like bank cameras) are often digital or have a certain resolution (number of pixels). When enlarged, if the image is a bitmap (composed of pixels) or has low resolution, increasing its size stretches the pixels, leading to loss of detail and blurriness. Also, if the original image capture had low quality (e.g., camera limitations, motion blur, low light causing noise), enlarging amplifies these issues as there's not enough original detail to support the larger size.
# Answer:
The image is blurry when enlarged because it likely has a limited resolution (number of pixels or detail in the original capture). Enlarging a low - resolution image (e.g., a bitmap image with fixed pixels) stretches the existing pixels, and there is insufficient original detail to maintain clarity at a larger size. Additionally, issues like motion blur or low - quality capture during the original image taking (due to camera limitations, poor lighting, etc.) are amplified when the image is enlarged, as there is no extra detail to fill in the expanded view.

### Question 2
# Explanation:
## Step 1: Recall the relationship between field of view (FOV) and magnification (M)
The field of view and magnification are inversely proportional. That is, $ \text{FOV}_1\times\text{M}_1=\text{FOV}_2\times\text{M}_2 $, where $ \text{FOV}_1 = 5.0\space\text{mm} $, $ \text{M}_1=60\times $, and $ \text{M}_2 = 25\times $, and we need to find $ \text{FOV}_2 $.
## Step 2: Rearrange the formula to solve for $ \text{FOV}_2 $
From $ \text{FOV}_1\times\text{M}_1=\text{FOV}_2\times\text{M}_2 $, we can get $ \text{FOV}_2=\frac{\text{FOV}_1\times\text{M}_1}{\text{M}_2} $
## Step 3: Substitute the values into the formula
Substitute $ \text{FOV}_1 = 5.0\space\text{mm} $, $ \text{M}_1 = 60 $, and $ \text{M}_2=25 $ into the formula: $ \text{FOV}_2=\frac{5.0\space\text{mm}\times60}{25} $
First, calculate $ 5.0\times60 = 300 $, then divide by 25: $ \frac{300}{25}=12.0\space\text{mm} $
# Answer:
The field of view at $ 25\times $ is $ 12.0\space\text{mm} $

### Question 3
To solve this, we need to know the field of view at $ 1000\times $. But since it's not given, we assume that we know the field of view diameter (let's call it $ D $) at $ 1000\times $. Then the diameter of the specimen ($ d $) is $ \frac{1}{3} $ of $ D $, so $ d=\frac{1}{3}D $.

For example, if the field of view at $ 1000\times $ is $ 1.5\space\text{mm} $ (a common value for some microscopes at high magnification), then the diameter of the specimen would be $ \frac{1}{3}\times1.5 = 0.5\space\text{mm} $. But since the field of view at $ 1000\times $ is not provided in the question, we can only give the formula:

If the field of view diameter at $ 1000\times $ is $ D $, then the diameter of the specimen $ d=\frac{1}{3}D $

# Answer:
Let the field of view diameter at $ 1000\times $ be $ D $. The diameter of the specimen is $ \boldsymbol{\frac{1}{3}D} $ (where $ D $ is the field of view diameter at $ 1000\times $). If a numerical value for $ D $ was provided, we could calculate the exact diameter. For example, if $ D = 1.5\space\text{mm} $, the diameter would be $ 0.5\space\text{mm} $.

### Question 4
# Brief Explanations:
1. **Focus Issue**: The microscope might not be properly focused when using the $ 40\times $ objective. The $ 4\times $ and $ 10\times $ objectives have a larger depth of field and may be in focus more easily, while the high - power $ 40\times $ objective has a very shallow depth of field, so a small error in focus can make the image disappear.
2. **Parfocality Problem**: The microscope may not be parfocal (where the image remains in focus when switching objectives). If the $ 40\times $ objective is not parfocal with the lower - power objectives, the image will go out of focus and may seem to disappear.
3. **Specimen Position**: The specimen (the letter "e") may have moved or not be centered in the field of view. The field of view is smaller at $ 40\times $ than at $ 4\times $ or $ 10\times $. If the "e" was near the edge of the field of view at lower magnifications, it may be outside the field of view at $ 40\times $.
4. **Condenser and Aperture Adjustment**: The condenser (which focuses light onto the specimen) and the aperture diaphragm may not be adjusted for the $ 40\times $ objective. For high - power objectives, the condenser needs to be raised and the aperture diaphragm adjusted to provide the correct amount of light and resolution. If not adjusted, the image may be too dark or lack resolution, making the "e" invisible.
5. **Dirty Objective or Slide**: The $ 40\times $ objective lens may be dirty, or the slide with the "e" may have smudges or debris on it, which is more noticeable at high magnification and can obscure the image.
# Answer:
Possible reasons why the "e" is not visible at $ 40\times $ are:
1. The microscope is not properly focused for the $ 40\times $ objective (shallow depth of field at high power makes focus errors more impactful).
2. The microscope is not parfocal, so the image goes out of focus when switching to $ 40\times $.
3. The "e" is not centered in the field of view, and the smaller field of view at $ 40\times $ excludes it.
4. The condenser and aperture diaphragm are not adjusted for the $ 40\times $ objective, leading to poor lighting or resolution.
5. The $ 40\times $ objective lens or the slide is dirty, obscuring the image.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step 1: Recall the relationship between field of view (FOV) and magnification (M)

Step 2: Rearrange the formula to solve for \( \text{FOV}_2 \)

Step 3: Substitute the values into the formula

Answer:

Question 2