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A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Question 1
A person suffers from hypermetropia (long sight). Use of a spectacle lens of power +2.0D allows the person to just see clearly an object placed 24 cm away from the e... show full transcript
Worked Solution & Example Answer:A person suffers from hypermetropia (long sight) - AQA - A-Level Physics - Question 1 - 2017 - Paper 5
Step 1
Explain why the unaided defective eye cannot form a clearly focused image of the object placed 24 cm from the eye.
Answer
The unaided eye of a person suffering from hypermetropia cannot focus properly because the eye's lens is not powerful enough to bend the incoming rays of light adequately. The rays coming from an object placed at 24 cm are not able to converge on the retina but instead focus behind it. This condition happens due to the eyeball being too short in length.
Step 2
Calculate the distance of the image formed from the spectacle lens. Give your answer to a suitable number of significant figures.
Answer
Using the lens formula: rac{1}{f} = rac{1}{d_o} + rac{1}{d_i} where
- f = rac{1}{P} = rac{1}{2} = 0.5 m (focal length of the lens),
- m (object distance).
Rearranging for : rac{1}{d_i} = rac{1}{f} - rac{1}{d_o} = rac{1}{0.5} - rac{1}{0.24} Calculating this gives: Thus, the distance of the image from the lens is 0.46 m when expressed to two significant figures.
Step 3
Step 4
Draw a ray diagram to show how this spectacle lens forms an image of the object placed 24 cm from the spectacle lens.
Answer
The ray diagram should include:
- An object placed 24 cm from the lens.
- Two rays drawn from the top of the object:
- One ray parallel to the principal axis which refracts through the focal point after passing through the lens.
- Another ray passing through the center of the lens which continues in a straight line.
- The point where the refracted rays converge to form an image on the opposite side of the lens.
Label the object, the image, and the principal focus of the lens.