Problems -41 and 42

41.- Think you want to print out a photograph with a size of DIN A4: 210 × 297 mm

maintaining a printing quality of 200 dpi. Which resolution would the image need?

To determine the resolution required for printing a photograph at a specific size and quality, you can use the formula:

$$\text{Resolution (in pixels)} = \text{Print size (in inches)} \times \text{DPI (dots per inch)}$$

First, we need to convert the dimensions of the paper from millimeters to inches:

$$1 \text{ inch} = 25.4 \text{ mm}$$

So:

• Width of DIN A4 paper: $210 \text{ mm} \div 25.4 = 8.27 \text{ inches}$
• Height of DIN A4 paper: $297 \text{ mm} \div 25.4 = 11.69 \text{ inches}$

Now, to calculate the resolution at 200 DPI:

• Width resolution: $8.27 \text{ inches} \times 200 \text{ DPI} = 1654 \text{ pixels}$
• Height resolution: $11.69 \text{ inches} \times 200 \text{ DPI} = 2338 \text{ pixels}$

So, for printing a photograph at 200 DPI on DIN A4 paper, the required resolution would be 1654 x 2338 pixels.

42.- Which resolution would the same picture need to have a 300 dpi picture?

To determine the resolution needed for a 300 DPI print, we'll follow the same steps as before but with the new DPI value of 300.

1. Convert paper size to inches:

• Width: $210 \, \text{mm} \div 25.4 = 8.27 \, \text{inches}$
• Height: $297 \, \text{mm} \div 25.4 = 11.69 \, \text{inches}$

2. Calculate the required resolution at 300 DPI:

• Width resolution: $8.27 \, \text{inches} \times 300 \, \text{DPI} = 2481 \, \text{pixels}$
• Height resolution: $11.69\text{inches}\times 300\text{DPI}=3507\text{pixels}$

To print the same image at 300 dpi on DIN A4 paper, the required resolution would be 2481 x 3507 pixels.