A flower is placed at a distance of 7.0 cm in front of a thin lens. The image distance is 12 cm. What is the focal length of the lens? Group of answer choices 5.7 cm 3.6 cm 5.1 cm 4.4 cm
The Correct Answer and Explanation is:
To determine the focal length of the lens, we can use the lens formula:1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}f1=do1+di1
Where:
- fff is the focal length of the lens (the value we are trying to find),
- dod_odo is the object distance (distance from the object to the lens),
- did_idi is the image distance (distance from the image to the lens).
Step 1: Understand the given information
- The object distance (dod_odo) is 7.0 cm.
- The image distance (did_idi) is 12 cm.
- Since the image is real (assuming the lens is converging), the image distance is positive.
Step 2: Substitute the given values into the lens formula
Substitute do=7.0 cmd_o = 7.0 \, \text{cm}do=7.0cm and di=12.0 cmd_i = 12.0 \, \text{cm}di=12.0cm into the lens equation:1f=17.0+112.0\frac{1}{f} = \frac{1}{7.0} + \frac{1}{12.0}f1=7.01+12.01
Step 3: Calculate the right side of the equation
First, calculate the reciprocal of the object distance:17.0=0.1429\frac{1}{7.0} = 0.14297.01=0.1429
Next, calculate the reciprocal of the image distance:112.0=0.0833\frac{1}{12.0} = 0.083312.01=0.0833
Now, sum the two values:0.1429+0.0833=0.22620.1429 + 0.0833 = 0.22620.1429+0.0833=0.2262
Step 4: Solve for fff
Now, solve for fff by taking the reciprocal of 0.2262:f=10.2262=4.42 cmf = \frac{1}{0.2262} = 4.42 \, \text{cm}f=0.22621=4.42cm
Step 5: Round the result
Rounding to one decimal place, the focal length is approximately 4.4 cm.
Final Answer:
The correct answer is 4.4 cm.
Explanation:
The focal length of a lens is determined by the relationship between the object distance and image distance, as described by the lens formula. For a real image formed by a converging lens, the focal length can be found by adding the reciprocals of the object and image distances and then taking the reciprocal of the sum. In this case, after performing the calculations, we determined that the focal length of the lens is approximately 4.4 cm.